The correct option is B 2
|z−1−i|=√2
This represents a circle with centre, C1(1,1) and radius r1=√2
|z+1+i|=2
This represents a circle with centre, C2(−1,−1) and radius r2=2
Now, C1C2=√22+22=2√2
r2+r1=2+√2r2−r1=2−√2
So, r2+r1>C1C2>r2−r1
Therefore, these two circles intersect at two points only.
Hence, there are two possible complex numbers satisfying the given equations.