The correct option is D (1−√74)+i(1+√74)
The given equation represents circles
(x−1)2+(y−1)2=2
and (x+1)2+(y+1)2=4
⇒C1(1,1),r1=√2,C2(−1,−1),r2=2
C1C2=√8=2.8,r1+r2=2+√2=3.41
C1C2<r1+r2 and also C1C2>r2−r1 and hence the two circles are intersecting at two points. The common two points will satisfy both.
Solving both equations,we get intersection points as (1+√74)+i(1−√74) and (1−√74)+i(1+√74)