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

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

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

Thanks, any help would be greatly appreciated!

Cheers.

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- Mar 25th 2011, 01:03 AMrorosingsongExpressing 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 $\displaystyle Z^{4}$ in polar form?

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

Thanks, any help would be greatly appreciated!

Cheers. - Mar 25th 2011, 01:04 AMProve It
Well, what are your answers?

- Mar 25th 2011, 03:13 AMrorosingsong
Mmmm... I got:

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

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

and

$\displaystyle \frac{1}{z} = \frac{\sqrt{2}}{6} ( cos(\frac{\pi }{4}) + i sin(\frac{\pi }{4})\right )$ - Mar 25th 2011, 03:32 AMmr fantastic
- Mar 25th 2011, 11:27 PMrorosingsong
Oh whoops... silly mistake, methinks.

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

Is that right? - Mar 25th 2011, 11:28 PMProve It
Yes

- Mar 26th 2011, 12:33 PMHallsofIvy
- Mar 26th 2011, 06:39 PMProve It