Question

If $z$ is a complex number such that $|z|\ge 2$, then the minimum value of $|z+\frac{1}{2}|$

• A. is strictly greater than $\frac{5}{2}$
• B. is strictly greater than $\frac{3}{2}$ but less than $\frac{3}{2}$
• C. is equal to $\frac{5}{2}$
• D. lie in the interval $(1,2)$

Answer 1

The correct option is A is strictly greater than $\frac{5}{2}$

$|z+\frac{1}{2}|\ge |z|+\frac{1}{2}$

$\ge 2+\frac{1}{2}$

$\ge \frac{5}{2}$