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Thread: Expressing complex numbers in polar form.

  1. #1
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    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 $\displaystyle Z^{4}$ in polar form?

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

    Thanks, any help would be greatly appreciated!

    Cheers.
    Last edited by mr fantastic; Mar 25th 2011 at 03:28 AM. Reason: Title.
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  2. #2
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    Well, what are your answers?
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  3. #3
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    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

    $\displaystyle \frac{1}{z} = \frac{\sqrt{2}}{6} ( cos(\frac{\pi }{4}) + i sin(\frac{\pi }{4})\right )$
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  4. #4
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    Quote Originally Posted by rorosingsong View Post
    Mmmm... I got:

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

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

    and

    $\displaystyle \frac{1}{z} = \frac{\sqrt{2}}{6} ( cos(\frac{\pi }{4}) + i sin(\frac{\pi }{4})\right )$ Mr F says: Correct.
    ..
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    Oh whoops... silly mistake, methinks.

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

    Is that right?
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    Yes
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    Quote Originally Posted by rorosingsong View Post
    Oh whoops... silly mistake, methinks.

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

    Is that right?
    Of course, adding $\displaystyle 2\pi$ to the argument does't change the value but gives $\displaystyle 324(cos(\pi)+ i sin(\pi))$, exactly what you had before.
    Last edited by mr fantastic; Mar 26th 2011 at 03:00 PM. Reason: Fixed math tag.
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  8. #8
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    Quote Originally Posted by HallsofIvy View Post
    Of course, adding $\displaystyle 2\pi$ to the argument does't change the value but gives $\displaystyle 324(cos(\pi)+ i sin(\pi))$, exactly what you had before.
    True, but it is not the correct application of DeMoivre's Theorem.
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