Question

Express \[z=8+8i\] in polar form and hence find \[z ^{8}\]?
I've done the first part, just don't know how to do the second part

Answer 1

Using de Moirves theorem thingy

Answer 2

I think it was something like:\[
[r(\cos(x)+i\sin(x))]^n = r^n(\cos(nx)+i\sin(nx))
\]

Answer 3

but they ask for the answer in polar form and I get a massive number :S
can you please help me out with the theorem?

Answer 4

@wio could you show me how the theorem works please? I keep getting a ridiculous number :/

Answer 5

What do you have for \(x\) or I suppose it's usually \(\theta\)

Answer 6

What are \(r\) and \(\theta\)?

Answer 7

\[\theta \] comes up as \[\frac{ \Pi }{ 4 }\]
r comes up as \[8\sqrt{2}\]

Answer 8

So what do you get for \(8\theta\) and for \(r^8\)?

Answer 9

\[r ^{8} = 128\]
and
\[8\theta \] = \[2\Pi \]

Answer 10

it asks for the polar form of; \[z ^{8} \]

Answer 11

Okay so you should be getting \[
128(\cos(2\pi)+i\sin(2\pi)) = 128((1)+i(0)) = 128
\]

Answer 12

does that make the polar form;
\[128CIS(2\Pi)\]

Answer 13

The polar form is just \(128\). The imaginary part is \(0\).

Answer 14

and the angle is what then?

Answer 15

The angle is \(2\pi = 0\).