Question

Evaluate
(1+i) /(1-i)

Answer 1

We can compute this by multiplying both numerator and denominator by the conjugate, 1+i, of the denominator.

(1+i1−i)⋅(1+i1+i)=1+2i+i21−i2

We know that i2=−1, so:

1+2i+i21−i2=1+2i−11−(−1)=2i2=i.