For |z−1|≤√2,...(i) z lies on and inside the circle of radius √2 units and centre (1,0) . For S2 , let z=x+iy Now (1−i)(z)=(1−i)(x+iy) =x+iy−ix+y=(x+y)+i(y−x) ∴Re[(1−i)z]=(x+y) , which is greater than or equal to one. i.e., x+y≥1⋅⋅⋅⋅⋅⋅⋅(ii) Also, for S3 Let z=x+iy ∴Im(z)=y , which is less than or equal to one. i.e., y≤1⋅⋅⋅⋅⋅⋅⋅(iii) Concept Draw the graph of Eqs. (i), (ii) and (iii) and then select the common region bounded by Eqs. (i), (ii) and (iii) for S1∩S2∩S3.