If z is any complex number satisfying `|z-3-2i|lt=2` then the maximum value of `|2z-6+5i|` is

Options

A. 3
B. 4
C. 5
D. `5//2`

Answer

C

Explanation

Clearly, any complex number z satisfying `|z-3-2i| le 2` lies inside or on the circle `|z-3-2i|=2`. We have to find the minimum of the distances of these points from the point P`(3,-5//2)`

Clearly, minimum distance is `AP=5/2`.
Hence, minimum value of `|2z-6+5i|` is `2AP=5`.