Question

For a complex number $Z$ , if $\left|Z-i\right|\le 2$ and $Z_1=5+3i$ , then the maximum value of $\left|iZ+Z_1\right|$ is (where, $i^2=-1$ )

• A. $7+\sqrt{13}$
• B. $7+\sqrt{12}$
• C. $7$
• D. $\sqrt{34}-2$

Answer 1

Answer: (C)

$\left|iZ+Z_1\right|=\left|i\left(Z-i\right)+\left(Z_1-1\right)\right|$
$\le \left|i\left(Z-i\right)\right|+\left|Z_1-1\right|$
$\le \left|i\right|\left|Z-i\right|+\left|4+3i\right|$
$\le 2+\sqrt{4^2+3^2}=7$