The number of complex numbers `z` satisfying `|z-3-i|=|z-9-i|a n d|z-3+3i|=3` are a. one b. two c. four d. none of these

Options

A. one
B. two
C. four
D. none of these

Answer

A

Explanation

Let `z = x +iy`. Then,
`|z-3-i|=|z-9-i|`
`rArr sqrt((x-3)^(2)+(y -1)^(2))=sqrt((x-9)^(2)+(y-1)^(2))`
`rArr x = 6`
`|z-3+3i|=3`
`rArr sqrt((x-3)^(2)+(y+3)^(2))=3`
For `x =6, y=-3`.
`therefore z =6-3i`