# Thread: Powers of complex numbers

1. ## Powers of complex numbers

Evaluate (2 + 2i)^8

Evaluate (2 + 2i)^8
Note that $(1+i)^2 = 1 +2i + i^2 = 2i$ and that $(2+2i)^8 = 2^8(1+i)^8$. Can you do it now?

(The answer is $2^{12}$.)

Evaluate (2 + 2i)^8
Have you studied the Binomial Theorem at all? Because that might be a "nicer" way to go, rather than doing all the multiplications by hand.

What have you tried? How far have you gotten? Where are you stuck?

4. Also, you could write z=2+2i as
$z= \sqrt{8}(cos(\frac{\pi}{4}) + i \, sin(\frac{\pi}{4}))$

So you get $z^{8}=8^{4} = 2^{12}$