Prove that cos z = 0 if and only if z = π/2 + kπ, where k is an integer.(adsbygoogle = window.adsbygoogle || []).push({});

The solution is :

cos z = (e^{iz}+e^{-iz})/2 = 0

<=>e^{iz}+e^{-iz})=0

<=>e^{2iz}=-1

<=>2iz=πi +2kπi

<=>z=π/2 + kπ

But i dont understand how does these 2 steps work

<=>e^{2iz}=-1

<=>2iz=πi +2kπi

how can a exp function suddenly become πi +2kπi

Thanks

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# Homework Help: Complex, exponential problem

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