Let, z=x+iy Given, 1≤|z−(1+i)|≤2 ⇒1≤|x+iy−1−i|≤2 ⇒1≤|(x−1)+i(y−1)|≤2 ⇒1≤√(x−1)2+(y−1)2≤2 It represent two concentric circle both have center at (1,1) and radius 1 and 2 .
Also given, |z−(1−i)|=1 ⇒|x+iy−1+i|=1 ⇒|(x−1)+i(y+1)|=1 ⇒√(x−1)2+(y+1)2=1 This represent a circle with center at (1,−1) and radius =1.