Question

If $|z+2-i|=5$ and maximum value of $|3z+9-7i|$ is $M$, then the value of $\frac{M}{4}$ is ____.

Answer 1

Given that $|z+2-i|=5$

Now, $|3z+9-7i|=3|z+2-i+(1-\frac{4i}{3})|\le 3(|z+2-i|+|1-\frac{4i}{3}|)=3(5+\frac{5}{3})=20$

Therefore, $\frac{M}{4}=5$

Ans: 5