Question

The maximum value of $|3z+9-7i|$ if $|z+2-i|=5$ is

• A. 10
• B. 15
• C. 20
• D. 5

Answer 1

The correct option is A 10

We have

$|z+2-i|=5$

$\Rightarrow z+2-i=5$

$\Rightarrow z=3+i$

Now, we have to find the maximum value of

$|3z+9-7i|$

$=|3(3+i)+9-7i$

$=|9+3i+9-7i|$

$|18-4i|$

$=10$

Hence, the option $\left(A\right)$ is correct.