Question

If z is any complex number satisfying $|z-3-2i|\le 2,$ then minimum value of $|2z-6+5i|$ is___

• A. 5
• B. 2.5
• C. 4.5
• D. 9

Answer 1

The correct option is A 5

Given $|z-3-2i|\le 2$
which represents a circular region with centre (3, 2) and radius 2.
Now $|2z-6+5i|=2|z-(3-\frac{5}{2}i)|$
$=2\times$ distance of z from P
(where Z lies in or on the circle)
Also min distance of z from $P=\frac{5}{2}$
$\therefore$ Minimum value of $|2z-6+5i|=5$