Complex Analysis: Theory and Applications · Problem 1.4.9

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · arg-reciprocal-not-negarg

Problem

Describe the set of complex numbers for which Arg ⁣(1z)≠−Arg(z)\text{Arg}\!\left(\dfrac{1}{z}\right) \neq -\text{Arg}(z). Prove your assertion.

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