Simplify 1+i1−i.
=1+i1−i⋅1−i1−i
=12−i21−2i−1
=1+1−2i
=2−2i
=−i
Simplify (1+i)8(1−i)9
(1+i)8(1−i)9=(1+i)8(1−i)8(1−i)=[(1+i)(1−i)]8(1−i)=[(1+i)(1−i)(1−i)(1−i)]8(1−i)=[1−i21−2i+i2]8(1−i)=[1−(−1)1−2i−1]8(1−i)=[2−2i]8(1−i)=(−i)8(1−i)=((−1)i)8(1−i)=((−1)8i8)(1−i)=(1⋅(i4)2)(1−i)=(1⋅(1)2)(1−i)=1⋅(1−i)=1−i