What are the greatest and least values of $|z_1-z_2|$ whereas $|z_2|=2,z_1=3+4i$ & $z_1,z_2$ are complex numbers?
$|z_2|=2$
$z_1=3+4i$
$|z_1-z_2|=?$
Let $z_2=a+bi$
After doing some manipulation I got $|z_1-z_2|=\sqrt{29-(6a+8b)}$
Now I have to find out the minimum of $6a+8b$ to get the maximum of $|z_1-z_2|$ & vice versa.
But How can I find those min & max , I'm not getting any ideas!!