Complex Analysis: Theory and Applications · Problem 1.4.7

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · arg-product-counterexample

Problem

Let z1=−1+i3z_1 = -1 + i\sqrt{3} and z2=−3+iz_2 = -\sqrt{3} + i. Show that the equation Arg(z1z2)=Arg z1+Arg z2\text{Arg}(z_1 z_2) = \text{Arg}\,z_1 + \text{Arg}\,z_2 does not hold for the specific choice of z1z_1 and z2z_2. Why not?

Browse the problem library