Use DeMoivre's Theorem to find the indicated power of the following complex number. (-3 + 3i)^4

Question

I know the formula, but it says to put exponents between sin/cos and theta. That's the main part that confuses me.

Answer 1

The easiest way to do this is to convert the complex number to polar form.

R = sqrt[(-3)² + 3²] = 3√2 and θ = arctan(-1) = 3π/4

Then the 4th power is R⁴ = 4*3⁴ and the other part is e^3πi = e^πi,

Now multiply the 2 together and you have your answer.

You can convert to the form with cos and sin then easily back to rectangular form.