Question

The n^th roots of any number are in ____________

(a) arithmetic progression

(b) geometric progression

(c) harmonic progression

(d) no specific pattern

I got this question during a job interview.

This intriguing question originated from Roots of Complex Numbers in chapter Complex Numbers of Engineering Mathematics

Answer 1

Correct answer is (b) geometric progression

For explanation I would say: We know that re^iα=re^i(α+2π). Hence, if re^iα/n is a n^th root of a number, then, re^ i(α/n+2π/n) is also a n^th root of that number. Hence, the roots are in G.P. with common ratio= e^i2π/n.