Let z be a complex number satisfying |z-3| |z-1|,|z-3| |z-5|,|z-i| |z+i| and |z-i| |z-5 i| . The area of the region in which z can lie is equal to

Step-by-step solution

array ll |z-3| |z-1| z+ z 4 x 2 & ( z+ z =2 x) |z-3| |z-5| z+ z 8 x 4 & ( z- z =2 i y) |z-i| |z+i| i(z- z ) 0 y 0 & |z-i| |z-5 i| i(z- z ) -6 y 3 . & array Clearly the region is a rectangle of area =2 3=6