Take the branch of $\log(z)$ to lie in $(-\pi, \pi]$. With complex numbers when does $\sqrt{z^2} = z$ hold and when doesn't it? If we take $z=-1$, this equality holds but then $1=-1$. I have a feeling that it is because $-1$ lies on the branch cut but I am still confused as to why this occurs?
2026-03-26 02:52:00.1774493520
Complex Analysis Branch cuts
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The function is considered to be undefined at the branch cut.