Click to edit Master title style
Click to edit Master text styles
Second level
Third level
Fourth level
Fifth level
‹date/time›
‹footer›
‹#›
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/master08.xml
Content-Transfer-Encoding: quoted-printable
Content-Type: text/xml; charset="utf-8"
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/preview.wmf
Content-Transfer-Encoding: base64
Content-Type: image/x-wmf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------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/pres.xml
Content-Transfer-Encoding: quoted-printable
Content-Type: text/xml; charset="utf-8"
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0090.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
Ó =
F r a n k M a
2 0 0 6
A complex number
is a number of the form
=
; &n=
bsp; =
;
a ± bi
where a and b are real numbers, a =
is called the real part and ±bi
is called the imaginary part
of the complex number =
Complex Numbers
Example B: 5 – 3i, 6i, -17 are complex numbers
for 6i =3D 0 + 6i, -17 =3D -17 + 0i=
.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0091.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
Ó =
F r a n k M a
2 0 0 6
A complex number
is a number of the form
=
; &n=
bsp; =
;
a ± bi
where a and b are real numbers, a =
is called the real part and ±bi
is called the imaginary part
of the complex number =
Complex Numbers
Example B: 5 – 3i, 6i, -17 are complex numbers
for 6i =3D 0 + 6i, -17 =3D -17 + 0i=
.
Every real number x is a complex number because
x =3D x + 0i.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0092.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
Ó =
F r a n k M a
2 0 0 6
A complex number
is a number of the form
=
; &n=
bsp; =
;
a ± bi
where a and b are real numbers, a =
is called the real part and ±bi
is called the imaginary part
of the complex number =
Complex Numbers
Example B: 5 – 3i, 6i, -17 are complex numbers
for 6i =3D 0 + 6i, -17 =3D -17 + 0i=
.
Every real number x is a complex number because
x =3D x + 0i.
The
absolute value <=
/span> of a ± bi, written as | a ±
bi|, is defined to be Öa 2 + b2 .
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0093.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
Ó =
F r a n k M a
2 0 0 6
A complex number
is a number of the form
=
; &n=
bsp; =
;
a ± bi
where a and b are real numbers, a =
is called the real part and ±bi
is called the imaginary part
of the complex number =
Complex Numbers
Example B: 5 – 3i, 6i, -17 are complex numbers
for 6i =3D 0 + 6i, -17 =3D -17 + 0i=
.
Every real number x is a complex number because
x =3D x + 0i.
The
absolute value <=
/span> of a ± bi, written as | a ±
bi|, is defined to be Öa 2 + b2 .
Example
C: |5 – 3i|
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0094.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
Ó =
F r a n k M a
2 0 0 6
A complex number
is a number of the form
=
; &n=
bsp; =
;
a ± bi
where a and b are real numbers, a =
is called the real part and ±bi
is called the imaginary part
of the complex number =
Complex Numbers
Example B: 5 – 3i, 6i, -17 are complex numbers
for 6i =3D 0 + 6i, -17 =3D -17 + 0i=
.
Every real number x is a complex number because
x =3D x + 0i.
The
absolute value <=
/span> of a ± bi, written as | a ±
bi|, is defined to be Öa 2 + b2 .
Example
C: |5 – 3i| =3D Ö 5 2 + 3 2 =3D Ö 34
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0110.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
Arithmetic of Complex Numbers
The most important complex numb=
er
multiplication is the =
conjugate-multiplication :
=
The complex numbers a + bi and a – bi are th=
e conjugate of each other.&n=
bsp;
For example 3 + 4i and
3
– 4i are conjugate of each other.
The conjugate of a real number is itself.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0111.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
(a + bi)(a – bi) =3D a 2 + b 2
Arithmetic of Complex Numbers
The most important complex numb=
er
multiplication is the =
conjugate-multiplication :
=
The complex numbers a + bi and a – bi are th=
e conjugate of each other.&n=
bsp;
For example 3 + 4i and
3
– 4i are conjugate of each other.
The conjugate of a real number is itself.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0112.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
(a
+ bi)(a – bi) =3D a 2 + b 2
Note that the product of a conjugate pair is alway=
s a positive real number .
Arithmetic of Complex Numbers
The most important complex numb=
er
multiplication is the =
conjugate-multiplication :
=
The complex numbers a + bi and a – bi are th=
e conjugate of each other.&n=
bsp;
For example 3 + 4i and
3
– 4i are conjugate of each other.
The conjugate of a real number is itself.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0113.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
(a
+ bi)(a – bi) =3D a 2 + b 2
Note that the product of a conjugate pair is alway=
s a positive real number .
Arithmetic of Complex Numbers
The most important complex numb=
er
multiplication is the =
conjugate-multiplication :
=
The complex numbers a + bi and a – bi are th=
e conjugate of each other.&n=
bsp;
For example 3 + 4i and
3
– 4i are conjugate of each other.
Example F: =
;
a. (4 – 3i)(4 + 3i)
The conjugate of a real number is itself.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0114.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
(a
+ bi)(a – bi) =3D a 2 + b 2
Note that the product of a conjugate pair is alway=
s a positive real number .
Arithmetic of Complex Numbers
The most important complex numb=
er
multiplication is the =
conjugate-multiplication :
=
The complex numbers a + bi and a – bi are th=
e conjugate of each other.&n=
bsp;
For example 3 + 4i and
3
– 4i are conjugate of each other.
Example F: =
;
a. (4 – 3i)(4 + 3i) =3D 42 + 32
The conjugate of a real number is itself.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0115.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
(a
+ bi)(a – bi) =3D a 2 + b 2
Note that the product of a conjugate pair is alway=
s a positive real number .
Arithmetic of Complex Numbers
The most important complex numb=
er
multiplication is the =
conjugate-multiplication :
=
The complex numbers a + bi and a – bi are th=
e conjugate of each other.&n=
bsp;
For example 3 + 4i and
3
– 4i are conjugate of each other.
Example F: =
;
a. (4 – 3i)(4 + 3i) =3D 42 + 32 =3D 25
The conjugate of a real number is itself.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0116.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
(a
+ bi)(a – bi) =3D a 2 + b 2
Note that the product of a conjugate pair is alway=
s a positive real number .
Arithmetic of Complex Numbers
The most important complex numb=
er
multiplication is the =
conjugate-multiplication :
=
The complex numbers a + bi and a – bi are th=
e conjugate of each other.&n=
bsp;
For example 3 + 4i and
3
– 4i are conjugate of each other.
Example F: =
;
a. (4 – 3i)(4 + 3i) =3D 42 + 32 =3D 25
b. ( Ö 7 – =
2i)( Ö 7 + 2i)
The conjugate of a real number is itself.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0117.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
(a
+ bi)(a – bi) =3D a 2 + b 2
Note that the product of a conjugate pair is alway=
s a positive real number .
Arithmetic of Complex Numbers
The most important complex numb=
er
multiplication is the =
conjugate-multiplication :
=
The complex numbers a + bi and a – bi are th=
e conjugate of each other.&n=
bsp;
For example 3 + 4i and
3
– 4i are conjugate of each other.
Example F: =
;
a. (4 – 3i)(4 + 3i) =3D 42 + 32 =3D 25
b. ( Ö 7 – =
2i)( Ö 7 + 2i) =3D ( Ö 7)2 + 22 =3D 11
The conjugate of a real number is itself.
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/slide0142.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
Arithmetic of Complex Numbers
The po=
wers
of i go in cycle as shown below:
i =3D=
i 5=
=3D i 9 ..
-1 =
=3D i 2=
=3D i 6 ..
-i =
=3D i 3=
=3D i 7 ..
1 =3D=
i 4=
=3D=
i8=
..<=
/span>
Example
H: Simplify i 59
59 =3D 4 * 14 + 3,
hence i 59 =3D i4 * 14+3 =3D i* 14+3 =3D ( i 4 ) 14 i3 =3D 1 14 i 3 =3D i =3D -i
numSlds )
gSldJumpIdx =3D numSlds;
if ( gSldJumpIdx >=3D 0 ) {
if ( gSldJumpIdx =3D=3D 0 )
gSldJumpIdx =3D 1;
var jumpTo =3D parseInt(gSldJumpIdx);
gSldJump =3D 0; gSldJumpIdx =3D "";
win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref )
}
}
}
function _KDH()
{
if( event.keyCode =3D=3D 8 ) {
event.returnValue =3D 0;
parent.GoToPrevSld();
}
}
function DocumentOnClick()
{
if( IsNts() || parent.HideMenu() ) return;
if( ( g_allowAdvOnClick && !parent.IsFramesMode() ) ||
(event && (event.keyCode=3D=3D32) ) )
parent.GoToNextSld();
}
var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""=
, g_bgSound=3D"",
g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser =
=3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1;
var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w=
indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va=
r g_animManager =3D null;
var g_animUseRuntime =3D false;
var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime;
var g_animMainSequence =3D null;
var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram=
es", gIsEndShow=3D0, NUM_VIS_SLDS=3D74, SCRIPT_HREF=3D"script.js", FULLSCR_=
HREF=3D"fullscreen.htm";
var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO=
tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true
window.gPPTHTML=3DSupportsPPTHTML()
var g_fBaseHyperlink =3D false;
var gMainDoc=3Dnew Array(new hrefList("slide0060.htm",1,-1,1),new hrefList(=
"slide0061.htm",1,-1,1),new hrefList("slide0059.htm",1,-1,1),new hrefList("=
slide0078.htm",1,-1,1),new hrefList("slide0079.htm",1,-1,1),new hrefList("s=
lide0080.htm",1,-1,1),new hrefList("slide0081.htm",1,-1,1),new hrefList("sl=
ide0082.htm",1,-1,1),new hrefList("slide0083.htm",1,-1,1),new hrefList("sli=
de0084.htm",1,-1,1),new hrefList("slide0085.htm",1,-1,1),new hrefList("slid=
e0086.htm",1,-1,1),new hrefList("slide0087.htm",1,-1,1),new hrefList("slide=
0071.htm",1,-1,1),new hrefList("slide0088.htm",1,-1,1),new hrefList("slide0=
089.htm",1,-1,1),new hrefList("slide0090.htm",1,-1,1),new hrefList("slide00=
91.htm",1,-1,1),new hrefList("slide0092.htm",1,-1,1),new hrefList("slide009=
3.htm",1,-1,1),new hrefList("slide0094.htm",1,-1,1),new hrefList("slide0075=
.htm",1,-1,1),new hrefList("slide0095.htm",1,-1,1),new hrefList("slide0096.=
htm",1,-1,1),new hrefList("slide0097.htm",1,-1,1),new hrefList("slide0098.h=
tm",1,-1,1),new hrefList("slide0099.htm",1,-1,1),new hrefList("slide0100.ht=
m",1,-1,1),new hrefList("slide0101.htm",1,-1,1),new hrefList("slide0102.htm=
",1,-1,1),new hrefList("slide0103.htm",1,-1,1),new hrefList("slide0104.htm"=
,1,-1,1),new hrefList("slide0105.htm",1,-1,1),new hrefList("slide0106.htm",=
1,-1,1),new hrefList("slide0107.htm",1,-1,1),new hrefList("slide0043.htm",1=
,-1,1),new hrefList("slide0108.htm",1,-1,1),new hrefList("slide0109.htm",1,=
-1,1),new hrefList("slide0110.htm",1,-1,1),new hrefList("slide0111.htm",1,-=
1,1),new hrefList("slide0112.htm",1,-1,1),new hrefList("slide0113.htm",1,-1=
,1),new hrefList("slide0114.htm",1,-1,1),new hrefList("slide0115.htm",1,-1,=
1),new hrefList("slide0116.htm",1,-1,1),new hrefList("slide0117.htm",1,-1,1=
),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide0118.htm",1,-1,1)=
,new hrefList("slide0119.htm",1,-1,1),new hrefList("slide0120.htm",1,-1,1),=
new hrefList("slide0121.htm",1,-1,1),new hrefList("slide0122.htm",1,-1,1),n=
ew hrefList("slide0123.htm",1,-1,1),new hrefList("slide0124.htm",1,-1,1),ne=
w hrefList("slide0125.htm",1,-1,1),new hrefList("slide0126.htm",1,-1,1),new=
hrefList("slide0127.htm",1,-1,1),new hrefList("slide0077.htm",1,-1,1),new =
hrefList("slide0128.htm",1,-1,1),new hrefList("slide0129.htm",1,-1,1),new h=
refList("slide0130.htm",1,-1,1),new hrefList("slide0131.htm",1,-1,1),new hr=
efList("slide0132.htm",1,-1,1),new hrefList("slide0133.htm",1,-1,1),new hre=
fList("slide0134.htm",1,-1,1),new hrefList("slide0135.htm",1,-1,1),new href=
List("slide0136.htm",1,-1,1),new hrefList("slide0137.htm",1,-1,1),new hrefL=
ist("slide0138.htm",1,-1,1),new hrefList("slide0139.htm",1,-1,1),new hrefLi=
st("slide0140.htm",1,-1,1),new hrefList("slide0141.htm",1,-1,1),new hrefLis=
t("slide0142.htm",1,-1,1),new hrefList("slide0076.htm",1,-1,1));
/*********************************************
Frameset functions
These functions control slide navigation
and state of the frameset.
**********************************************/
function RemoveFilePrefixFromHref(href)
{
var regExp =3D /^file:\/\/\//i;
return href.replace(regExp, "")
}
function FullScrInit()
{
g_allowAdvOnClick =3D GetCurSld().mAdvOnClk
document.body.style.backgroundColor=3D"black"
document.oncontextmenu=3Dparent._CM;
document.onkeydown =3D _KDH;
document.ondragstart=3DCancel
document.onselectstart=3DCancel
self.focus()
}
function Redirect( frmId )
{=09
var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId()
if(idx>=3D0) str=3Dstr.substr(1);
if( window.name !=3D frmId && ( sId !=3D str) ) {
obj =3D GetObj("Main-File")
window.location.href=3Dobj.href+"#"+sId
return 1
}
return 0
}
var MHTMLPrefix =3D CalculateMHTMLPrefix();=20
function CalculateMHTMLPrefix()
{
if ( document.location.protocol =3D=3D 'mhtml:') {=20
href=3Dnew String(document.location.href)=20
Start=3Dhref.indexOf('!')+1=20
End=3Dhref.lastIndexOf('/')+1=20
if (End < Start)=20
return href.substring(0, Start)=20
else=20
return href.substring(0, End)=20
}
return '';
}
function GetTags(base,tag)
{
if(g_supportsPPTHTML) return base.all.tags(tag);
else return base.getElementsByTagName(tag);
}
function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP=
refix+GetHrefObj( gCurSld ).mNtsHref ) }
function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() }
function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() }
function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() }
function SetHasNts( fVal )
{
if( gHasNts !=3D fVal ) {
gHasNts=3DfVal
UpdNavPane()
}
}
function ToggleOtlText()
{
gOtlTxtExp=3D!gOtlTxtExp
UpdOtlPane()
}
function ClearMedia()
{
// Clear any sounds playing before launching another browser window. Other=
wise,
// in fullscreen mode, you'll continue to hear the sound in the frames mod=
e.
if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0;
}
function FullScreen()
{=20
if ( PPTSld.g_animUseRuntime )
PPTSld.document.body.pause();
ClearMedia();
var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF =
: FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref;
if (MHTMLPrefix !=3D "")
href =3D RemoveFilePrefixFromHref(href)
if(PPTNav.event.ctrlKey) {
var w =3D (window.screen.availWidth * 1.0) / 2.0
var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW
win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top=
=3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h );
if( win.document.body && PPTSld.g_animUseRuntime )
win.document.body.PPTSldFrameset=3Dwindow;
}
else
{
win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" );
if( win.document.body && PPTSld.g_animUseRuntime )
win.document.body.PPTSldFrameset=3Dwindow;
}
}
function ToggleVNarration()
{
rObj=3DPPTSld.document.all("NSPlay")
if( rObj && !PPTSld.g_animUseRuntime ) {
if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) )
rObj.Play()
else if( rObj.playState =3D=3D 2 )
rObj.Pause()
else
return;
}
else if( PPTSld.g_animUseRuntime )
{
narObj =3D PPTSld.document.all("narrationID")
if( narObj )
narObj.togglePause()
}
}
function GetCurSldNum()
{ =20
obj=3DGetHrefObj(gCurSld)
if( obj.mOrigVis =3D=3D 1 )
return obj.mSldIdx
else =20
return gCurSld
}
function GetNumSlds()
{ =20
if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 )
return GetSldList().mNumVisSlds;
else
return GetSldList().mList.length
}
function GetSldNum( href )
{
for(ii=3D0; ii 1 )
PopSldList();
else if( !IsFramesMode() ) {
if( gLoopCont )
GoToFirst()
else
EndShow()
}
}
function GoToPrevSld()
{
ii=3DgCurSld-1
if( ii > 0 ) {
obj=3DGetHrefObj(ii)
while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) )
obj=3DGetHrefObj(--ii)
if( ii =3D=3D 0 ) ii=3D1
GoToSldNum(ii)
}
}
function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) }
function GoToLast()
{
ii=3DGetSldList().mList.length
if( ii !=3D gCurSld )
GoToSld( GetHrefObj(ii).mSldHref )
}
function GoToSldNum( num )
{
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
obj =3D GetHrefObj( num )
obj.mVis=3D1
gPrevSld=3DgCurSld
gCurSld =3D num;
=09
if (MHTMLPrefix !=3D "")
PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref=
))
else
PPTSld.location.replace(obj.mSldHref)
=09
if( IsFramesMode() ) {
UpdNavPane(); UpdOtlPane(); UpdNtsPane()
}
}
function GoToSld( href )
{
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
GetHrefObj( GetSldNum(href) ).mVis=3D1
if (MHTMLPrefix !=3D "")
PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href))
else
PPTSld.location.replace(href)
}
function SldUpdated( id )
{
if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return
gPrevSld=3DgCurSld
gCurSld=3DGetSldNum(id)
if( IsFramesMode() ) {
UpdNavPane(); UpdOtlPane(); UpdNtsPane()
}
}
function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) }
function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO=
bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) }
function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) }
function CloseWindow() {
if( HideMenu() ) return;
=09
var event =3D PPTSld.event;
if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D=
=3D32 || event.type=3D=3D"click" ) )
window.close( self );
CatchNumKeys( self, event );
}
function Unload() { gIsEndShow=3D0; }
function SetupEndShow() {
gIsEndShow=3D1;
PPTSld.document.body.scroll=3D"no";
PPTSld.document.onkeypress=3DCloseWindow;
PPTSld.document.onclick=3DCloseWindow;
PPTSld.document.oncontextmenu=3D_CM;
}
function EndShow()
{
if( IsFramesMode() ) return
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
doc=3DPPTSld.document
var dir =3D doc.body.dir
if( dir !=3D "rtl" ) dir =3D "ltr";
doc.open()
doc.writeln('' + ENDSHOW_MESG + '
0) {
PushSldList(sldList,fEnd);
gCurSld =3D 1;
}
else
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
}
function PushSldList(arr,fEnd) {
var ii =3D gSldStack.length;
gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd);
GoToSld( gSldStack[ii].mList[0].mSldHref );
}
function PopSldList() {
if (gSldStack[gSldStack.length-1].fEndShow)
EndShow()
else {
gCurSld =3D gSldStack[gSldStack.length-1].mCurSld;
gSldStack[gSldStack.length-1] =3D null;
gSldStack.length--;
var sldList =3D gSldStack[gSldStack.length-1];
GoToSld( sldList.mList[gCurSld - 1].mSldHref );
}
}
var custShowList=3Dnew Array();
/*********************************************
Navigation button implementation
There are 2 types of buttons: ImgBtn, TxtBtn
implemented as function objects. They share
a similiar interface so the event handlers
can call SetActive, for example, on a button=20
object without needing to know exactly=20
what type of button it is.
**********************************************/
//----------------------------------
function ImgBtn( oId,bId,w,action )
//----------------------------------
{
var t=3Dthis
t.Perform =3D _IBP
t.SetActive =3D _IBSetA
t.SetInactive=3D _IBSetI
t.SetPressed =3D _IBSetP
t.SetDisabled=3D _IBSetD
t.Enabled =3D _IBSetE
t.ChangeIcon =3D null
t.UserAction =3D action
t.ChgState =3D _IBUI
t.mObjId =3D oId
t.mBorderId=3D bId
t.mWidth =3D w
t.mIsOn =3D t.mCurState =3D 0
}
function _IBSetA()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
obj.style.posTop=3D0
}
}
function _IBSetI()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
obj.style.posTop=3D0=20
}
}
function _IBSetP()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 )
obj.style.posLeft+=3D1; obj.style.posTop+=3D1
}
}
function _IBSetD()
{ =20
obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 )
obj.style.posTop=3D0=20
}
function _IBSetE( state )
{
var t=3Dthis
GetObj( t.mBorderId ).style.visibility=3D"visible"
if( state !=3D t.mIsOn ) {
t.mIsOn=3Dstate
if( state )
t.SetInactive()
else
t.SetDisabled()
}
}
function _IBP()
{
var t=3Dthis
if( t.mIsOn ) {
if( t.UserAction !=3D null )
t.UserAction()
if( t.ChangeIcon ) {
obj=3DGetObj(t.mObjId)
if( t.ChangeIcon() )
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth
else
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth
}
t.SetActive()
} =20
}
function _IBUI( clr1,clr2,nextState )
{
var t=3Dthis
SetBorder( GetObj( t.mBorderId ),clr1,clr2 )
obj=3DGetObj( t.mObjId )
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj=
.style.posTop
t.mCurState=3DnextState
return obj
}
//-----------------------------------------
function TxtBtn( oId,oeId,action,chkState )
//-----------------------------------------
{
var t=3Dthis
t.Perform =3D _TBP
t.SetActive =3D _TBSetA
t.SetInactive=3D _TBSetI
t.SetPressed =3D _TBSetP
t.SetDisabled=3D _TBSetD
t.SetEnabled =3D _TBSetE
t.GetState =3D chkState
t.UserAction =3D action
t.ChgState =3D _TBUI
t.mObjId =3D oId
t.m_elementsId=3D oeId
t.mIsOn =3D 1
}
function _TBSetA()
{
var t=3Dthis
if( t.mIsOn && !t.GetState() )
t.ChgState( gHiliteClr,gShadowClr,0,0 )
}
function _TBSetI()
{
var t=3Dthis
if( t.mIsOn && !t.GetState() )
t.ChgState( gFaceClr,gFaceClr,0,0 )
}
function _TBSetP()
{
if( this.mIsOn )
this.ChgState( gShadowClr,gHiliteClr,1,1 )
}
function _TBSetD()
{ =20
this.ChgState( gFaceClr,gFaceClr,0,0 )
this.mIsOn =3D 0
}
function _TBSetE()
{
var t=3Dthis
if( !t.GetState() )
t.ChgState( gFaceClr,gFaceClr,0,0 )
else
t.ChgState( gShadowClr,gHiliteClr,1,1 )
t.mIsOn =3D 1
}
function _TBP()
{
var t=3Dthis
if( t.mIsOn ) {=20
if( t.UserAction !=3D null )
t.UserAction()
if( !t.GetState )
return
if( t.GetState() )
t.SetPressed()
else
t.SetActive()
} =20
}
function _TBUI( clr1,clr2,lOffset,tOffset )
{
SetBorder( GetObj( this.mObjId ),clr1,clr2 )
Offset( GetObj( this.m_elementsId ),lOffset,tOffset )
}
function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle=
ft }
function SetBorder( obj, upperLeft, lowerRight )
{
s=3Dobj.style;
s.borderStyle =3D "solid"
s.borderWidth =3D 1=20
s.borderLeftColor =3D s.borderTopColor =3D upperLeft
s.borderBottomColor=3D s.borderRightColor =3D lowerRight
}
function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] }
function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() }
function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() }
function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() }
function BtnOnUp()
{
b=3DGetBtnObj()
if( b !=3D null )
b.Perform()
else
Upd()
}
function GetNtsState(){ return parent.gNtsOpen }
function GetOtlState(){ return parent.gOtlOpen }
function GetOtlTxtState(){ return parent.gOtlTxtExp }
function NtsBtnSetFlag( fVal )
{
s=3Ddocument.all.item( this.m_flagId ).style
s.display=3D"none"
if( fVal )
s.display=3D""
else
s.display=3D"none"
}
function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etActive() }
function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etInactive() }
function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etPressed() }
function _BSetA_BorderImg()
{=20
b =3D gBtnArr[this.mBorderId]=20
if( b !=3D null && this.mIsOn && !b.GetState() ) {
obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
obj.style.posTop=3D0
}
}
function _BSetI_BorderImg()
{=20
b =3D gBtnArr[this.mBorderId]
if( b !=3D null && this.mIsOn && !b.GetState() ) {
obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
obj.style.posTop=3D0
}
}
var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"=
THREEDFACE"
var gBtnArr =3D new Array()
gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan=
e,GetOtlState )
gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt=
lPane,GetOtlState )
gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN=
tsPane )
gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg;
gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg;
gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.=
ToggleNtsPane,GetNtsState )
gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To=
ggleNtsPane,GetNtsState )
gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n=
b_prevBorder",30,parent.GoToPrevSld )
gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n=
b_nextBorder",30,parent.GoToNextSld )
gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent=
.FullScreen )
gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa=
rent.FullScreen,null )
gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent=
.FullScreen,null )
gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice=
","nb_voiceBorder",18,parent.ToggleVNarration )
gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT=
xt","nb_otlTxtBorder",23,parent.ToggleOtlText )
gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts"
gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag
gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState
/*********************************************
Context menu implementation
_CM() is the function that's hooked up to
the oncontextmenu event. Once we're asked to
show the menu, we first build it by creating
DIVs on-the-fly. Then we position it=20
within the screen area so it doesn't get
clipped.
Creating the DIVs using createElement() means
we don't have to write out any extra HTML
into the slide HTML files.
**********************************************/
var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr=
row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval"
function ShowMenu()
{
BuildMenu();
var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y=
=3DPPTSld.event.clientY+doc.scrollTop
m =3D PPTSld.document.all.item("ctxtmenu")
m.style.pixelLeft=3Dx
if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) )
m.style.pixelLeft=3Dx-m.scrollWidth
m.style.pixelTop=3Dy
if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) )
m.style.pixelTop=3Dy-m.scrollHeight
m.style.display=3D""
}
function _CM()
{
if( !parent.IsFullScrMode() ) return;
if(!PPTSld.event.ctrlKey) {
ShowMenu()
return false
} else
HideMenu()
}
function BuildMenu()
{
if( PPTSld.document.all.item("ctxtmenu") ) return
var mObj=3DCreateItem( PPTSld.document.body )
mObj.id=3D"ctxtmenu"
mObj.style.visibility=3D"hidden"
var s=3DmObj.style
s.position=3D"absolute"
s.cursor=3D"default"
s.width=3D"120px"
SetCMBorder(mObj,"menu","black")
var iObj=3DCreateItem( mObj )
SetCMBorder( iObj, "threedhighlight","threedshadow" )
iObj.style.padding=3D2
CreateMenuItem( iObj,sNext,M_GoNextSld,M_True )
CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld )
=09
CreateSeparator( iObj )
CreateMenuItem( iObj,sEnd,M_End,M_True )
mObj.style.visibility=3D"visible"
}
function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa=
lue=3Dfalse }
function Highlight() { ChangeClr("activecaption","threedhighlight") }
function Deselect() { ChangeClr("threedface","menutext") }
function Perform()
{
e=3DPPTSld.event.srcElement
if( e.type=3D=3D"menuitem" && e.IsActive() )
e.Action()
else
PPTSld.event.cancelBubble=3Dtrue
}
function ChangeClr( bg,clr )
{
e=3DPPTSld.event.srcElement
if( e.type=3D=3D"menuitem" && e.IsActive() ) {
e.style.backgroundColor=3Dbg
e.style.color=3Dclr
}
}
function M_HasPrevSld() { return( parent.HasPrevSld() ) }
function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() }
function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();=
PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() }
function M_True() { return true }
function M_End() { window.close( self ) }
function CreateMenuItem( node,text,action,eval )
{
var e=3DCreateItem( node )
e.type=3D"menuitem"
e.Action=3Daction
e.IsActive=3Deval
e.innerHTML=3Dtext
if( !e.IsActive() )
e.style.color=3D"threedshadow"
e.onclick=3DPerform
e.onmouseover=3DHighlight
e.onmouseout=3DDeselect
s=3De.style;
s.fontFamily=3DsFont
s.fontSize=3D"9pt"
s.paddingLeft=3D2
}
function CreateSeparator( node )
{
var sObj=3DCreateItem( node )
SetCMBorder(sObj,"menu","menu")
var s=3DsObj.style
s.borderTopColor=3D"threedshadow"
s.borderBottomColor=3D"threedhighlight"
s.height=3D1
s.fontSize=3D"0px"
}
function CreateItem( node )
{
var elem=3DPPTSld.document.createElement("DIV")
node.insertBefore( elem )
return elem
}
function SetCMBorder( o,ltClr,rbClr )
{
var s=3Do.style
s.backgroundColor=3D"menu"
s.borderStyle=3D"solid"
s.borderWidth=3D1
s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr
}
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/fullscreen.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/buttons.gif
Content-Transfer-Encoding: base64
Content-Type: image/gif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------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/frame.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Complex Numbers
------=_NextPart_01C7E520.5C0EB390
Content-Location: file:///C:/7102A2B3/1ComplexNumbers_files/outline.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
No=
tes
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Addition and subtraction of complex numbers:
23
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
24
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
25
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
26
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
27
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
28
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
29
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
30
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
31
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
32
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
33
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
34
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
35
Addition and subtraction of complex numbers:
To add or subtract complex numbers, treat the i as a variable.
36
37
38
39
40
(a + bi)(a – bi) =3D a2 + b2
41
(a + bi)(a – bi) =3D a2 + b2
Note that the product of a conjugate pair is always a positive real
number.
42
(a + bi)(a – bi) =3D a2 + b2
Note that the product of a conjugate pair is always a positive real
number.
43
(a + bi)(a – bi) =3D a2 + b2
Note that the product of a conjugate pair is always a positive real
number.
44
(a + bi)(a – bi) =3D a2 + b2
Note that the product of a conjugate pair is always a positive real
number.
45
(a + bi)(a – bi) =3D a2 + b2
Note that the product of a conjugate pair is always a positive real
number.
46
(a + bi)(a – bi) =3D a2 + b2
Note that the product of a conjugate pair is always a positive real
number.
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
HW
P399 57-73 odd, =
89-94
all
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
<=
a
href=3D"slide0126_image039.gif">
=
=
=
=
=
=
![](3D"slide0092_image024.gif")
![](3D"slide0093_image025.gif")
![](3D"slide0094_image026.gif")
![](3D"slide0094_image027.gif")
![](3D"slide0142_image067.gif")
![](3D"notes_flag.gif")
No=
tes![](3D"buttons.gif")
![](3D"slide0078_image001.gif"){kind=link}
![](3D"slide0079_image002.gif"){kind=link}
![](3D"slide0079_image003.gif"){kind=link}
![](3D"slide0080_image004.gif"){kind=link}
![](3D"slide0080_image005.gif"){kind=link}
![](3D"slide0081_image006.gif"){kind=link}
![](3D"slide0081_image007.gif"){kind=link}
![](3D"slide0082_image008.gif"){kind=link}
![](3D"slide0082_image009.gif"){kind=link}
![](3D"slide0083_image010.gif"){kind=link}
![](3D"slide0083_image011.gif"){kind=link}
![](3D"slide0084_image012.gif"){kind=link}
![](3D"slide0084_image013.gif"){kind=link}
![](3D"slide0085_image014.gif"){kind=link}
![](3D"slide0085_image015.gif"){kind=link}
![](3D"slide0085_image016.gif"){kind=link}
![](3D"slide0086_image017.gif"){kind=link}
![](3D"slide0086_image018.gif"){kind=link}
![](3D"slide0086_image019.gif"){kind=link}
![](3D"slide0087_image020.gif"){kind=link}
![](3D"slide0087_image021.gif"){kind=link}
![](3D"slide0087_image022.gif"){kind=link}
![](3D"slide0087_image023.gif"){kind=link}
![](3D"slide0098_image001.gif"){kind=link}
![](3D"slide0099_image002.gif"){kind=link}
![](3D"slide0100_image006.gif"){kind=link}
![](3D"slide0101_image007.gif"){kind=link}
![](3D"slide0102_image008.gif"){kind=link}
![](3D"slide0103_image009.gif"){kind=link}
![](3D"slide0104_image010.gif"){kind=link}
![](3D"slide0105_image011.gif"){kind=link}
![](3D"slide0106_image012.gif"){kind=link}
![](3D"slide0107_image013.gif"){kind=link}
![](3D"slide0119_image001.gif"){kind=link}
![](3D"slide0120_image002.gif"){kind=link}
![](3D"slide0120_image003.gif"){kind=link}
![](3D"slide0121_image004.gif"){kind=link}
![](3D"slide0121_image005.gif"){kind=link}
![](3D"slide0121_image006.gif"){kind=link}
![](3D"slide0121_image007.gif"){kind=link}
![](3D"slide0121_image008.gif"){kind=link}
![](3D"slide0122_image009.gif"){kind=link}
![](3D"slide0122_image010.gif"){kind=link}
![](3D"slide0122_image011.gif"){kind=link}
![](3D"slide0122_image012.gif"){kind=link}
![](3D"slide0122_image013.gif"){kind=link}
![](3D"slide0122_image014.gif"){kind=link}
![](3D"slide0123_image015.gif"){kind=link}
![](3D"slide0123_image016.gif"){kind=link}
![](3D"slide0123_image017.gif"){kind=link}
![](3D"slide0123_image018.gif"){kind=link}
![](3D"slide0123_image019.gif"){kind=link}
![](3D"slide0123_image020.gif"){kind=link}
![](3D"slide0123_image021.gif"){kind=link}
![](3D"slide0124_image022.gif"){kind=link}
![](3D"slide0124_image023.gif"){kind=link}
![](3D"slide0124_image024.gif"){kind=link}
![](3D"slide0124_image025.gif"){kind=link}
![](3D"slide0124_image026.gif"){kind=link}
![](3D"slide0124_image027.gif"){kind=link}
![](3D"slide0125_image028.gif"){kind=link}
![](3D"slide0125_image029.gif"){kind=link}
![](3D"slide0125_image030.gif"){kind=link}
![](3D"slide0125_image031.gif"){kind=link}
![](3D"slide0125_image032.gif"){kind=link}
![](3D"slide0125_image033.gif"){kind=link}
![](3D"slide0125_image034.gif"){kind=link}
![](3D"slide0126_image035.gif"){kind=link}
![](3D"slide0126_image036.gif"){kind=link}
![](3D"slide0126_image037.gif"){kind=link}
![](3D"slide0126_image038.gif"){kind=link}
![](3D"slide0126_image039.gif"){kind=link}
![](3D"slide0126_image040.gif"){kind=link}
![](3D"slide0126_image041.gif"){kind=link}
![](3D"slide0126_image042.gif"){kind=link}
![](3D"slide0127_image043.gif"){kind=link}
![](3D"slide0127_image044.gif"){kind=link}
![](3D"slide0127_image045.gif"){kind=link}
![](3D"slide0127_image046.gif"){kind=link}
![](3D"slide0127_image047.gif"){kind=link}
![](3D"slide0127_image048.gif"){kind=link}
![](3D"slide0127_image049.gif"){kind=link}
![](3D"slide0127_image050.gif"){kind=link}
![](3D"slide0127_image051.gif"){kind=link}
![](3D"slide0127_image052.gif"){kind=link}
![](3D"slide0128_image053.gif"){kind=link}
![](3D"slide0129_image054.gif"){kind=link}
![](3D"slide0130_image055.gif"){kind=link}
![](3D"slide0131_image056.gif"){kind=link}
![](3D"slide0132_image057.gif"){kind=link}
![](3D"slide0133_image058.gif"){kind=link}
![](3D"slide0134_image059.gif"){kind=link}
![](3D"slide0135_image060.gif"){kind=link}
![](3D"slide0136_image061.gif"){kind=link}
![](3D"slide0137_image062.gif"){kind=link}
![](3D"slide0138_image063.gif"){kind=link}
![](3D"slide0139_image064.gif"){kind=link}
![](3D"slide0140_image065.gif"){kind=link}
![](3D"slide0141_image066.gif"){kind=link}