Mathematics - Complex Number Question with Solution | TestHub

$\left|z-1\right|\le \left|z+i\right|$
Putting$z=x+iy$and simplifying, we get$x+y\ge 0$
The region in shown shaded right side of the line$x+y=0$



The largest value of$r$would be the length of perpendicular from$A\left(4,1\right)$, on the line$x+y=0$

$\left|\frac{4+1}{\sqrt{2}}\right|= \frac{5}{\sqrt{2}}$$= \frac{5}{2}\sqrt{2}$