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Q.
If $z$ is a complex number such that $|z|\geq\,2$, then the minimum value of $ |z + (1/2) | $
Complex Numbers and Quadratic Equations
Solution:
$|z| \ge 2$ is the region lying on or outside the circle with centre $(0,0)$ and radius $2$.
$\left|z+\frac{1}{2}\right|$ is the distance of $'z'$ from $\left(-\frac{1}{2}, 0\right)$ which lies inside the circle.
$\therefore $ min. $\left|z+\frac{1}{2}\right| =$ distance of $\left(-\frac{1}{2}, 0\right)$ from
$\left(-2, 0\right)=\frac{3}{2} \in\left(1, 2\right)$
