Question

The set of points in an argand diagram which satisfy both $\left|z\right|\le 4$ and
arg $z=\pi /3$ is

• A. a circle and a line
• B. a radius of a circle
• C. a sector of a circle
• D. an infinite part line

Answer 1

Answer: (C)

a sector of a circle

$|z|\le 4$ represents all the interior region of a circle of radius $4$ and center origin.
Similarly, $argz=\frac{\pi }{3}$ represents all points on the line making ${60}^o$ with $x$ axis in anticlockwise direction.
Hence option c becomes correct.