Question

If $|z-i|\le 2$ and $\alpha =5+3i$, then find the maximum value of $|iz+\alpha |$.

Answer 1

$|iz+z_0|=\left|i\right(z-1)-1+5+3i|$

$=\left|i\right(z-i)+4+3i|$

$\le |\left|i\right||2-i|+|4+3i||$

$|iz+z_0|\le 7$