The function $z^n$ pass $n$ times by the same point in the complex plane of the codomain, if $f(z)=z^n$, each $z_n=\sqrt[n]{r}.e^{i.(\frac{\theta}{n}+\frac{2.\pi}{n})}$ has the same image (right?), so the branch cuts that I should take to make this function injective is $\alpha\lt arg(z)\lt\alpha+\frac{2.\pi}{n}$?
2026-03-25 01:41:14.1774402874
Branch points of $z^n$
95 Views Asked by user655901 https://math.techqa.club/user/user655901/detail AtRelated Questions in COMPLEX-ANALYSIS
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