Question

Find the possible value(s) of Re(i^1/2)+|Im(i^1/2)|.

(a) -1, 1

(b) 0, √2

(c) 0, 1

(d) 1, √2

This question was addressed to me in an online quiz.

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

Answer 1

The correct choice is (b) 0, √2

Best explanation: We can write: i=e^iπ/2⇒i^1/2=e^iπ/4=1/√2+i/√2, also i^1/2=e^i3π/4=-1/√2-i/√2

Hence, Re(i^1/2)+|Im(i^1/2)|=1/√2+1/√2=√2 OR -1/√2+1/√2=0.