Question

If z lies on the circle $\left|z\right|=1$, then $\frac{2}{z}$ lies on

• A. Circle
• B. Straight line
• C. Parabola
• D. None of these

Answer 1

The correct option is A Circle

Given $z$ lies on the circle $|z|=1$

$|\frac{2}{z}|=\frac{|2|}{|z|}=\frac{2}{|z|}=\frac{2}{1}=2$

$⟹|\frac{2}{z}|=2$

$⟹\frac{2}{z}$ also lies on the circle