If a2+b2=1, then 1+b+ia1+b−ia

Given that a2 + b2 = 1. Therefore,1+b+ia1+b−ia=(1+b+ia)(1+b+ia)(1+b−ia)(1+b+ia)=(1+b)2−a2+2ia(1+b)1+b2+2b+a2=1−a2+2b+b2+2ia(1+b)2(1+b)=2b2+2b+2ia(1+b)2(1+b)=b+ia