Question

Let z=(sqrt3)-i and w=-2-2i.
A. Convert Z and W to polar form.
B. Calculate WZ using De Moivre's theorem. Express your answer in polar (r(cos(theta)+isin(theta))) form.
C. Calculate z^2. Express your answer in rectangular (a+bi) form.
D. Calculate w^4. Express your answer in polar (r(cos(theta)+isin(theta))) form.

Answer 1

@geerky42 Think you can help a brony out?

Answer 2

Need help with A?

Answer 3

Actually, I finished this one. But I could use help with the next one!

Answer 4

Find the complex fourth roots of 81(cos(3pi/8)+isin(3pi/8))
A: Find the fourth root of 81.
B: Divide the angle in the problem by 4 to find the first argument.
C: Use the fact that adding 2pi to the angle 3pi/8 produces the same effective angle to generate the other three possible angles for the fourth roots. Be sure that your angles lie between 0 and 2pi.
D: Find all 4 of the fourth roots of 81(cos(3pi/8)+isin(3pi/8)) Express your answers in polar (r(cos(theta)+isin(theta))) form.