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What is $|\frac{(\pi+i)^{100}}{(\pi-i)^{100}}|$
I am stuck on this question, I have to get rid of the denominator before I can apply $|z|=\sqrt{a^2+b^2}$ but I don't know how to do that because of the exponents. I also thought of converting the part inside the parenthesis to polar coordinates but I don't think that would work either.

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First note that $\big| \dfrac{z}{w} \big| = \dfrac{|z|}{|w|}$ so you can calculate the modulus of each term separately and divide them.
But observe that $\overline{\pi + i} = \pi - i$ and $|z| = |\bar z|$

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    since the numerator and denominator are conjugates, let's call the modulus of ($\pi+i$) = $\alpha$ and since $|z|=|\bar{z}|$ we have $(\frac{\alpha}{\alpha})^{100}$ and this equals $1$ – 2017-02-05
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    That is correct, and you avoided unnecessary calculations :) – 2017-02-05
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$|z|^N=|z^N|$

Now it is your turn

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    thank you, this also helped – 2017-02-05