Posted by **BreAnne** on Wednesday, May 23, 2012 at 12:41am.

6. Compute the modulus and argument of each complex number. I did a-c and f.

D. -5

E. -5+5i

G. -3-4i

7. Let z= -5sqrt3/2+5/2i and w= 1+sqrt3i

a. convert z and w to polar form

b. calculate zw using De Moivres Theorem

c. calculate (z/w) using De M's theorem

Please help with these two problems? I did 1-6 and 9-10 already.

- trig -
**Reiny**, Wednesday, May 23, 2012 at 4:11am
6. I will do E, you try the others the same way

let z = -5 + 5i

modulus z = |z| = √((-5)^2 + 5^2) = √50 = 5√2

argument:

tanØ = 5/-5 = -1, where Ø is in quad II

Ø = 135°

G. is done the same way

for D, think of it as -5 + 0i

- trig -
**Reiny**, Wednesday, May 23, 2012 at 4:23am
7.

z = -5√3/2 + 5/2i

= 5(-√3/2 + (1/2)i )

argument :

tan Ø = (1/2) / (-√3/2), where Ø is in II

tan Ø = -1/√3

Ø = 150° or 5π/6 radians

z = 5(cos 150° + isin 150°) or 5(cos 5π/6 + isin 5π/6)

in the same way:

w = √10(cos 60°+ isin 60°) or √10(cos π/3 + isin π/3)

- trig -
**Reiny**, Wednesday, May 23, 2012 at 4:31am
b) to multiply two complex numbers in complex form

if u = r1(cos Ø1 + isinØ1) and v = r2(cosØ2 + isinØ2)

then uv = r1r2(cos(Ø1+Ø2) + isin(Ø1+Ø2)

and u/v = r1/r2 (cos(Ø1-Ø2) + isin(Ø1-Ø2)

so

(z)(w) = 5√10(cos (150+60) + isin(150+60)

= 5√10(cos 210° + isin 210°)

do z/w using the above definition.

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