Question

Let a and b be complex cube roots of unity. If x=7a+2b and y=2a+7b, then evaluate xy.

(a) 9

(b) 39

(c) 45

(d) 53

I had been asked this question during an interview.

My question comes from Roots of Complex Numbers in section Complex Numbers of Engineering Mathematics

Answer 1

Right answer is (d) 53

The best explanation: Write a=ω and b=ω^2.

Now, xy=(7a+2b)(2a+7b)=(7ω+2ω^2)(2ω+7ω^2)=14ω^2+14ω+53=39 (since, 1+ω+ω^2=0).