If z is a complex number such that z ≠ 0 and Re (z) = 0, then Im (z^2) = 0.

Question

State True of False:

If z is a complex number such that z ≠ 0 and Re (z) = 0, then Im (z²) = 0.

Answer 1

False

Explanation:

Given z ≠ 0 and Re (z) = 0

Let z = x + iy

Then x = 0

∴ z = iy

⇒ Im (z²) = i²y² = -y² ≠ 0