Math 240 Test 5 Su/97

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Math 240 Sample 5

1. Find algebraically (4 + 3i)( 2 = 211; 5i) A= ns: 23-14i

2. Find algebraically (4 + 3i)( 2 = 211; 5i)(4 – 3i)(2 + 5i) = Ans: 725

3. Find algebraically _{Ans: =
i}

4. Fin= d the polar form of the complex numbers (use a calaulator)

&= nbsp; a. 4 – 3i = = &nb= sp; b.= -3 – i = &nb= sp; = c. -<= span style=3D'mso-char-type:symbol;mso-symbol-font-family:Symbol'>Ö<= /span>3 – i <= o:p>

Ans: (5, -40), (5, 320) = (<= span style=3D'mso-char-type:symbol;mso-symbol-font-family:Symbol'>Ö<= /span>10, 198), (-<= /span>Ö10, 18) = &nb= sp; (2, 210), (-2, 30)

5. Con= vert 6cis(-60^o) into the rectangular from of a complex number. Ans: 3 – Ö10

6. Find the product of -3cis(45^{o<=
/sup>)*5cis(225^o)
in polar form and write the answer in the rectangular form}

&= nbsp; Ans: -15cis(270) =3D 15i

7. Fin= d the product of 3cis(45^o)*5cis(225^o) by converting each in= to the rectangular form first then convert your answer into the polar form. Ans: 15cis(270) =3D – 15i

8. Find the quotient _{in polar form first.&nbs=
p;
Then convert the answer into the rectangular form.=}

Ans: Ö2 + i<= span style=3D'font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-han= si-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman";letter-spacing:-.1= 5pt; mso-char-type:symbol;mso-symbol-font-family:Symbol'>Ö2<= /span>

9. Find (2 – 2i)⁸ us= ing the cis-form. Give the answer= in both the polar form and the standard form.

Ans: 4096<= o:p>

10. Fi= nd all solutions for r⁴=3D -16. Ans: cis(45), cis(135), cis(225), cis(315)

11. Co= nvert the following polar equations into rectangular equations<= /p>

a. r =3D 3 cosq = &nb= sp; = b. r (1 – sin= q) =3D 5 = = c. r =3D 3cosq + 5sinq

12. Co= nvert the following rectangular equations into polar equations<= /p>

a. x – 3y =3D 6 = = b. x² – y² =3D 5 = &nb= sp; c. x² ̵= 1; xy + y² =3D 2

13. Sk= etch the graph of

a. r =3D 3 cosq = b. r =3D 3cos2q = = c. r =3D 2 + 2 cosq =

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