Question

If the complex number \( z \) lies on a circle with center at the origin and radius \( \frac{1}{4} \), then the complex number \( 1 + z \) lies on a circle with radius

• A. 2
• B. \( \frac{3}{4} \)
• C. \( \frac{5}{4} \)
• D. \( \frac{7}{4} \)

Hint:

The transformation \( z \to 1 + z \) shifts the circle by 1 unit, changing its radius accordingly.

Answer 1

The Correct Option is C

The complex number \( z \) lies on a circle with radius \( \frac{1}{4} \), and when adding 1 to \( z \), the radius becomes the sum of the radius of \( z \) and the distance from 1 to the origin.