Question

Let \(z_1\) and \(z_2\) be two complex numbers, then :

• A. \(\left|\frac{z_1}{z_2}\right| < \frac{|z_1|}{|z_2|}\) for \(|z_2| \ne 0\)
• B. \(\left|\frac{z_1}{z_2}\right| \ne \frac{|z_1|}{|z_2|}\)
• C. \(|z_1 z_2| = |z_1||z_2|\)
• D. \(|z_1 z_2| < |z_1||z_2|\)

Hint:

Remember the modulus properties:
- Multiplication and division are perfectly preserved: \(|z_1 z_2| = |z_1||z_2|\) and \(\left|\frac{z_1}{z_2}\right| = \frac{|z_1|}{|z_2|}\).
- Addition and subtraction follow the triangle inequality: \(|z_1 + z_2| \le |z_1| + |z_2|\) and \(|z_1 - z_2| \ge ||z_1| - |z_2||\).

Answer 1

The Correct Option is C