Question

Find the cube root of 8i lying in the first quadrant of the complex plane.

(a) i-√3

(b) 2i+√3

(c) i+2√3

(d) i+√3

This question was addressed to me during an internship interview.

Origin of the question is Roots of Complex Numbers in portion Complex Numbers of Engineering Mathematics

Answer 1

The correct choice is (d) i+√3

Easy explanation: Let z^3=8i⇒z^3=-8i^3⇒[z/(-2i)]^3=1.

⇒z/(-2i)=1 or ω or ω^2⇒z=-2i or -2iω or -2iω^2

⇒z=-2i or i+√3 or i-√3 out of which i+√3 lies in the first quadrant.