Suppose that z1=6-8i. Find:

Question

A. The Trig Form of the complex number z1, where your theta is in degrees.

B. The Trig form of z1*z2, where
z2=5[cos(60degrees)+isin(60degrees)]

C. The Trig Form of (z1)^4

Answer 1

looks like z1 is in QIV, since x>0 and y<0

so, θ = 360 - arctan(8/6) = 360 - 53.1 = 306.9°

z1 = 10 cis 306.9°

z2 = 5 cis 60°

z1*z2 = 10*5 cis (-53.1+60) = 50 cis 6.9°

z1^4 = 10^4 cis 4*(-53.1)
= 10000 cis -212.4°
= 10000 cis 147.6°

x = 10000 cos 147.6° = -8443
y = 10000 sin 147.6° = 5358

z1^4 = -8443 + 5359i