Hi, I have recently started learning about complex numbers and the complex plane, and there is something I don't quite understand. Why is it that for every number [itex] z \in C [/itex](adsbygoogle = window.adsbygoogle || []).push({});

[itex] e^{i\theta} = z [/itex]

we have

[itex] \sqrt { [Re(z)]² + [Im(z)]² } = 1 [/itex] ?

Except for [itex] \theta = \frac {\pi}{2} or \frac {3\pi}{2} [/itex] of course. In other words, why do all numbers z define a unit circle's radius ?

Any help would be very much appreciated

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# Complex exponents

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