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

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

### Solution

$\frac{1+i}{1-i}$

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

$\frac{1+i}{1-i} X \frac{1+i}{1+i}$

= $\frac{1+2i+i^{2}}{1-i^{2}}$

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

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

=$\frac{2i}{2}$

= i

$\frac{1+i}{1-i}$= i