Question

A complex number \( z \) is such that \( \arg \left( \frac{-2}{3} + \frac{2i}{3} \right) = \frac{\pi}{3} \). The points representing this complex number will lie on

• A. an ellipse
• B. a parabola
• C. a circle
• D. a straight line

Hint:

The argument of a complex number is the angle it forms with the positive real axis in the complex plane.

Answer 1

The Correct Option is C

Step 1: Understanding the condition.
The argument of a complex number is given by the angle it makes with the real axis. The given condition indicates that the complex number lies on a circle.

Step 2: Conclusion.
The correct answer is that the complex number lies on a circle, corresponding to option (3).