Question

If $|z-i|\le 2$ and $z_0=13+5i$ then the maximum value of $|iz+z_0|$ is

• A. 15
• B. -15
• C. $2+\sqrt{194}$
• D. $\sqrt{194}-2$

Answer 1

The correct option is A 15

$|z-i|\le 2$
z lies on and in the inner part of the circle $|z-i|\le 2$
$z_0=13+5i$
From the fig:
$max\left(|iz+z_0|\right)$ will be the distance between point A & point B=[radius of circle (r)] + [distance between point A and center of the circle (d(AC))].
$max\left(|iz+z_0|\right)=max\left(|z-i{z}_0|\right)=max\left(|z-(-5+13i)|\right)=r+d\left(AC\right)$
$\Rightarrow max\left(|iz+z_0|\right)=2+\sqrt{{(0-(-5))}^2+{(1-13)}^2}=15$
Ans: A