# How do you simplify (1)/(1+i)?

Jun 22, 2018

$\frac{1 - i}{2}$

#### Explanation:

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

You multiply by the complex conjugate the denominator with the sign changed:

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

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

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

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

$\frac{1 - i}{1 - {\sqrt{- 1}}^{2}}$

$\frac{1 - i}{1 - \left(- 1\right)}$

$\frac{1 - i}{2}$

Jun 23, 2018

color(maroon)(=> (1 - i)/2

#### Explanation:

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

$\implies \left(\frac{1}{91} + i\right) \cdot \left(\frac{1 - i}{1 - i}\right) , \text{ rationalizing the denominator, by multiplying & Dividing by the conjugate of the denominator}$

$\implies \frac{1 - i}{1 - {i}^{2}}$

$\implies \left(\frac{1}{2}\right) - \frac{i}{2} , \text{ as } {i}^{2} = - 1$