Question

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

Answer 1

Correct Answer - 5
Given `|z-3-2i| le 2 `
To find minimum of |2z-6 +5 i|
or `2|z-3+5/2i|` using triangle inequality
ie. `||z_1|-|z_2||le|z_1+z_2|`
`therefore |z-3+5/2i|=|z-3-2i+2i+5/2i|`
`=|(z-3-2i)+9/2i|`
`ge |z-3-2i-9/2| ge|2-9/2|ge5/2`
`rArr" |z-3+5/2i|ge5/2or|2z-6+5i|ge5`