Question

If a > 0, a R, z = a + 2i and |z| = -az + 1, then:

• A. z is always a positive real number
• B. z is always a negative real number
• C. z is purely imaginary number
• D. such a complex z does not exist

Hint:

Modulus of a complex number is always real and non-negative.

Answer 1

The Correct Option is D

Step 1: Modulus property. |z| is always non-negative real.
Step 2: Contradiction. Equation leads to imaginary RHS, hence impossible.