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Math Help - finding powers of a complex number

  1. #1
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    finding powers of a complex number

    I am checking to see if this is correct?

    Use Demoivre's Theorem to find the indicated power of the complex number.

    <br />
(\sqrt(3) - i)^9<br />

    <br />
2^9[(cos 9*\pi/6 + i \sin 9*\pi/6)]<br />

    <br />
512(0+(-1))= -512<br />
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by robasc View Post
    I am checking to see if this is correct?

    Use Demoivre's Theorem to find the indicated power of the complex number.

    <br />
(\sqrt(3) - i)^9<br />

    <br />
2^9[(cos 9*\pi/6 + i \sin 9*\pi/6)]<br />

    <br />
512(0+(-1))= -512<br />
    \begin{aligned}\left(\sqrt{3}-i\right)^9&=\left(2\cos\left(\frac{\pi}{6}\right)-2i\sin\left(\frac{\pi}{6}\right)\right)^9\\<br />
&=2^9\left(\cos\left(\frac{-\pi}{6}\right)+i\sin\left(\frac{-\pi}{6}\right)\right)^9\\<br />
&=2^9e^{\frac{-9i\pi}{6}}\\<br />
&=2^9\left(\cos\left(\frac{-9\pi}{6}\right)+i\sin\left(\frac{-9\pi}{6}\right)\right)\\<br />
&=2^9(0--i)\\<br />
&=512i\end{aligned}
    Last edited by Mathstud28; December 10th 2008 at 08:48 PM.
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