If complex number z lies on the curve |z−(−1+i)|=1, then the locus of the complex  number ω=z+i1−i,i=−1 is a circle having

We have |z−(−1+i)|=1⇒|z+1−i|=1 Now, ω=z+i1−i⇒(1−i)ω=z+iadding -2i+1 on both sides⇒(1−i)ω−2i+1=z+1−i⇒|(1−i)ω−2i+1|=|z+1−i|⇒|1−i|ω+1−2i1−i=1⇒ω+(1−2i)(1+i)(1+i)(1−i)=12⇒ω−−3+i2=12