Complex Analysis: Theory and Applications · Problem 1.4.8

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · arg-product-half-plane

Problem

Show that the equation Arg(z1z2)=Arg z1+Arg z2\text{Arg}(z_1 z_2) = \text{Arg}\,z_1 + \text{Arg}\,z_2 is true provided that the inequalities −π2<Arg z1≤π2-\dfrac{\pi}{2} < \text{Arg}\,z_1 \leq \dfrac{\pi}{2} and −π2<Arg z2≤π2-\dfrac{\pi}{2} < \text{Arg}\,z_2 \leq \dfrac{\pi}{2} are satisfied. Describe the set of points that meets this criterion.

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