If Z=3+i2, then Z101+i103105 is equal to

Given, z=3+i2=i[1−i3]2=−iw Consider, z101+i103=(−iw)101+i103=−iw2−i=iw Now, z101+i103105=(iw)105=i Also z=−iwz2=(−iw)2=i2w2=−w2z3=(−iw)3=−i3⋅w3=iz101+i103=z3