Question

For the complex number z the minimum value of $|Z|+|Z-\frac{\sqrt{3}}{2}-\frac{i}{2}|$ is

Answer 1

${[|z|+|z-(\frac{\sqrt{3}}{2}+\frac{i}{2})|]}_{min}$
$=|\frac{\sqrt{3}}{2}+\frac{1}{2}i|$
$=\sqrt{\frac{3}{4}+\frac{1}{4}}=\sqrt{\frac{4}{4}=1}$