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I'm having trouble with this problem:

[tex] \left| \frac{(\pi + i)^{100}}{(\pi - i)^{100}} \right| = \ \ ? [/tex]

My first thought was, "put it in polar form and simpify," but that is not helping.

For the numerator pi + i :

[tex] r = \sqrt{\pi^2 + 1} [/tex]

[tex] \theta = \arctan{ \frac{1}{\pi} } [/tex] = ???

I don't see how this will help, it's not an easy one to put in polar form

I can also see that the numerator and denominator are complex conjugates, so maybe that is the starting point. But I can't see how to proceed

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# Homework Help: Powers of Complex Numbers

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