Question

Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form
a + bi.)

(2-2i)^7

Answer 1

thematically, as in trying to turn it into something based around angle and magnitude, it goes like this

\((2-2i)^7\)
\(\Rightarrow 2^7(1-i)^7\)
\(\Rightarrow 2^7 \sqrt{2}^7(\frac{1}{\sqrt2}-\frac{i}{\sqrt2} ~ i)^7 \) etc

so you've got \( \dfrac{\pi}{4}\) in there and a magnitude...

Answer 2

1. Write 2 - 2i in r*(cosθ + i*sinθ ) form.

2. Apply DeMoivre's Theorem.

If you have difficulty, look at examples and discussion here:

http://tinyurl.com/bg9pt9q

Answer 3

As a last resort, look at the worked problem here

: http://tinyurl.com/hjsbfmd