Problem #PRU-61175

Problems Algebra Algebra Complex numbers

Problem

Let \(z_1\) and \(z_2\) be fixed points of a complex plane. Give a geometric description of the sets of all points \(z\) that satisfy the conditions:

a) \(\operatorname{arg} \frac{z - z_1}{z - z_2} = 0\);

b) \(\operatorname{arg} \frac{z_1 - z}{z - z_2} = 0\).