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Math Help - Square Root of complex number

  1. #1
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    Square Root of complex number

    Is there a formula to find the square root of a complex number? I can't find it anywhere... Thanks.
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  2. #2
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    See...

    de Moivre's formula - Wikipedia, the free encyclopedia

    ... 'Applications'... a complex number z \ne 0 has two distinct square roots...

    Kind regards

    \chi \sigma
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  3. #3
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    The easiest way is to convert the complex number to exponential form, because

    \left(r\,e^{i\theta}\right)^{\frac{1}{2}} = r^{\frac{1}{2}}e^{\frac{1}{2}i\theta}.

    Note that this only gives you one of the square roots, but you can use the fact that the roots will be evenly placed around a circle to find the other.
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