The correct option is C only two solutions
Putting z = x + iy in the given equations, we have
and |z−3|=√2i.e.(x−3)2+y2=2…… (2)
Solving equations (1) and (2), we have y = -1, 1 and corresponding x = 2, 4 Hence, there are only two solutions, viz.
z = 2 - I, 4 + i