Question

Let \(Z_1\) and \(Z_2\) be two complex numbers, then:

• A. \(\overline{Z_1 + Z_2} \le \overline{Z_1} + \overline{Z_2}\)
• B. \(\overline{Z_1 + Z_2} \ge \overline{Z_1} + \overline{Z_2}\)
• C. \(\overline{Z_1 Z_2} = \overline{Z_1} \cdot \overline{Z_2}\)
• D. \(\overline{Z_1 Z_2} < \overline{Z_1} \cdot \overline{Z_2}\)

Hint:

Conjugation is a distributive operation over standard arithmetic.
This means that for any complex numbers \(Z_1\) and \(Z_2\):
- \(\overline{Z_1 \pm Z_2} = \overline{Z_1} \pm \overline{Z_2}\)
- \(\overline{Z_1 \cdot Z_2} = \overline{Z_1} \cdot \overline{Z_2}\)
- \(\overline{(Z_1 / Z_2)} = \overline{Z_1} / \overline{Z_2}\)

Answer 1

The Correct Option is C