Square Root of complex number

**jzellt** · October 11th 2010, 09:35 PM

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

**chisigma** · October 11th 2010, 09:49 PM

See...

de Moivre's formula - Wikipedia, the free encyclopedia

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

Kind regards

$\chi$ $\sigma$

**Prove It** · October 12th 2010, 12:50 AM

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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