Question

State True or False for the following:

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

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Let z = x + yi, z ≠ 0 and Re(z) = 0

Since real part is 0.

⇒ x = 0

∴ z = 0 + yi = yi

∴ lm(z²) = y²i²

= –y² which is real.