Question

On the arg and plane, the complex numbers z1, z2, z3, z4 are the vertices of a parallelogram. Evaluate (z4–z1+z2)/z3 .

(a) 1

(b) 2

(c) 3

(d) 4

This question was addressed to me during an interview for a job.

This key question is from Regions in the Complex Plane topic in chapter Complex Numbers of Engineering Mathematics

Answer 1

The correct choice is (a) 1

Explanation: For a parallelogram, the diagonals bisect each other. Hence, their midpoints coincide.

This implies that (z1+z3)/2=(z2+z4)/2 ⇒ z1+z3=z2+ z4 ⇒ ( z4– z1+ z2)/ z3=1.