Complex Analysis: Theory and Applications · Problem 5.2.4

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · logarithm-theorem-proof

Problem

Refer to Theorem 5.2. ((a)) Explain why −π<Arg(z1)+Arg(z2)≤π-\pi < \mathrm{Arg}(z_1) + \mathrm{Arg}(z_2) \leq \pi implies that Arg(z1z2)=Arg(z1)+Arg(z2)\mathrm{Arg}(z_1 z_2) = \mathrm{Arg}(z_1) + \mathrm{Arg}(z_2). ((b)) Prove the ``only if'' part.

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