Question

Let z1 and z2 be two complex numbers such that |z1 + z2| =| z1| + |z2 |. Then show that arg (z1) – arg (z2) = 0.

Answer 1

Let z1 = r1 (cosθ1 + i sin θ1) and z2 = r2 (cosθ2 + i sin θ2)

where r1 = z1 , arg (z1) = θ1, r2 = |z2| , arg (z2) = θ2.

We have,