Question

For two complex numbers p and q, if Arg(p)-Arg(q)=π/2 as well as |pq|=1, what is the value of p̅q ?

(a) -i

(b) -1

(c) i

(d) 1

I had been asked this question in an internship interview.

This question is from Complex Conjugates topic in portion Complex Numbers of Engineering Mathematics

Answer 1

Correct answer is (a) -i

Best explanation: p̅q=|p|e^-iarg p×|q|e^iarg q

                            = e^-i(arg p-arg q) (since |pq|=1)

                            = e^-iπ/2=-i.