How do you calculate (1 + i)/(1-i)?

We have to evaluate \(\frac{1+i}{1-i}\)

Solution

We will multiply Numerator and Denominator by ( 1 +i)

= \(\frac{1+2i+i^{2}}{1-i^{2}}\)

We know that i2= -1. On substituting in above equation we get

=\(\frac{1+2i-1}{1-(-1)}\)

=\(\frac{2i}{2}\)

= i

Answer