# Finding the largest set where a complex function is analytic

f(z) = e^z / (sinz - cosz)

So I solved for sinz - cosz = 0 and got pi/4. But why is it Pi/4 + kpi and not Pi/4 + k2pi for the part of the complex plane where this function is not analytic.

Thanks.

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$$\sin z -\cos z=0\Longleftrightarrow \tan z = 1\Longrightarrow z=\frac{\pi}{4}+k\pi\,\,,\,k\in\Bbb Z$$
as the period of the tangent function is $\,\pi\,$ , not $\,2\pi\,$