# Thread: Expressing complex numbers in polar form.

1. ## Expressing complex numbers in polar form.

Hi, I'm not too sure with this one, can I get some help?

If Z= 3 - 3i;what are Z, 1/Z and $Z^{4}$ in polar form?

I'm not sure if my answers are correct...

Thanks, any help would be greatly appreciated!

Cheers.

3. Mmmm... I got:

$z = 3\sqrt{2}\left ( cos(-\frac{\pi }{4}) + i sin(-\frac{\pi }{4})\right )$

$z^{4} = 324\left ( cos(\pi) + i sin(\pi)\right )$

and

$\frac{1}{z} = \frac{\sqrt{2}}{6} ( cos(\frac{\pi }{4}) + i sin(\frac{\pi }{4})\right )$

4. Originally Posted by rorosingsong
Mmmm... I got:

$z = 3\sqrt{2}\left ( cos(-\frac{\pi }{4}) + i sin(-\frac{\pi }{4})\right )$ Mr F says: Correct.

$z^{4} = 324\left ( cos(\pi) + i sin(\pi)\right )$ Mr F says: Argument is wrong. How did you get it?

and

$\frac{1}{z} = \frac{\sqrt{2}}{6} ( cos(\frac{\pi }{4}) + i sin(\frac{\pi }{4})\right )$ Mr F says: Correct.
..

5. Oh whoops... silly mistake, methinks.

$z^{4} = 324 (cos(-\pi )+ i sin(-\pi ))$

Is that right?

6. Yes

7. Originally Posted by rorosingsong
Oh whoops... silly mistake, methinks.

$z^{4} = 324 (cos(-\pi )+ i sin(-\pi ))$

Is that right?
Of course, adding $2\pi$ to the argument does't change the value but gives $324(cos(\pi)+ i sin(\pi))$, exactly what you had before.

8. Originally Posted by HallsofIvy
Of course, adding $2\pi$ to the argument does't change the value but gives $324(cos(\pi)+ i sin(\pi))$, exactly what you had before.
True, but it is not the correct application of DeMoivre's Theorem.