Question

The locus of the complex number z such that $arg\left(\frac{z-2}{z+2}\right)=\frac{\pi }{3}$ is:

• A. A circle
• B. A straight line
• C. A parabola
• D. An ellipse

Answer 1

The correct option is A A circle

arg $\frac{z-2}{z+2}$ = $\frac{\pi }{3}$

arg (z-2) - arg(z+2) = $\frac{\pi }{3}$

now z can be a segment of circle because in a segment of circle angle remains constant .