Question

The product of two complex numbers each of unit modulus is also a complex number, of.

• A. Unit modulus
• B. Less than unit modulus
• C. Greater than unit modulus
• D. None of these

Answer 1

Answer: (A)

Unit modulus

Answer 2

If $(\because|z| = |\overline{z}|)$and $= |{\overline{z}}_{1} + \overline{z_{2}} + ..... + {\overline{z}}_{n}| = \left| \frac{1}{z_{1}} + \frac{1}{z_{2}} + .... + \frac{1}{z_{n}} \right|$ then $z_{k} = \cos\theta_{k} + i\sin\theta_{k},k = 1,2,....n$