Question

If z is a complex number, then

A. |z²| > |z|²
B. |z²| = |z|²
C. |z²| < |z|²
D. |z²| ≥ |z|²

Answer 1

B. |z|² = |z²|

Given z is a complex number.

Let z = x + yi

⇒ |z| = |x + yi| and |z|² = |x + yi|²

⇒ |z|² = x² + y² … (1)

Now z² = x² + y²i² + 2xyi

⇒ z² = x² – y² + 2xyi

So, |z|² = x² + y² = |z|²

∴ |z|² = |z²|