Question

What is the shape of the region formed by the set of complex numbers z satisfying |z-ω|≤ α?

(a) circle of radius ω

(b) circle with center ω

(c) disk of radius α

(d) disk with center α

The question was asked in a national level competition.

The origin of the question is Regions in the Complex Plane topic in division Complex Numbers of Engineering Mathematics

Answer 1

The correct option is (d) disk with center α

The best explanation: The equation |z-ω|≤ α implies that the distance of z from ω is less than or equal to α. This means that a disk is formed with center ω and radius α.