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Thread: Another difficult complex number question

  1. #1
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    [Solved] Another difficult complex number question

    The question:

    If $\displaystyle z = re^{i\theta}, 0 \le \theta \le \frac{\pi}{2}$, show that $\displaystyle |(1 - i)z^2| = \sqrt{2}r^2$

    EDIT: I worked it out. It's actually really easy. >_<

    For those interested:

    $\displaystyle (1 - i) = \sqrt{2}e^{-i\frac{\pi}{4}}$
    $\displaystyle z^2 = r^2e^{i2\theta}$
    Multiplying both gives $\displaystyle \sqrt{2}r^2e^{-i\frac{\pi}{4}+{2\theta}}$
    Since we want the modulus, we get $\displaystyle \sqrt{2}r^2$
    Last edited by Glitch; Aug 14th 2010 at 02:46 AM.
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  2. #2
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    You should change the title to [Solved]Another difficult complex number question.
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