I think that $\sqrt{z}$ is not defined on $[-1,0]$ , but this is the function I got as a result in problem to map conformally unit disc on upper unit disc... Can anybody help me?
2026-03-26 01:07:42.1774487262
Does function $f(z)=-i\sqrt{z}$ map unit disc to upper disc?
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For every complex number $z$, there are two possible "square roots". One of them is the opposite of the other. Your question depends on which one you are considering.