Question

If a complex number z, with integral real and imaginary parts, satisfies z^2+ z̅^2=16, then find the value of |z|.

(a) 2^1/2

(b) 4

(c) 8^1/2

(d) 10^1/2

This question was addressed to me in an online interview.

My doubt is from Complex Conjugates in division Complex Numbers of Engineering Mathematics

Answer 1

Correct choice is (d) 10^1/2

Easy explanation: Let z=x+iy, then, x^2–y^2=8 (by replacing z by x+iy in the given equation)

Since, x and y are integers, |x|=3 and |y|=1 are the only possible values.

Therefore, |z|=(3^2+1^2)^1/2=10^1/2.