Question

The number of complex numbers z satisfying $|z-3-i|=|z-9-i|$ and $|z-3+3i|=3$ are

• A. one
• B. two
• C. four
• D. none oh these

Answer 1

The correct option is A one

$|z-3-i|=|z-9-i|$
$|z-3+3i|=3$
It can be observed from the figure that the given curves intersect only at one point.
Therefore only one solution exists.
Hence, option 'A' is correct.