# How do you simplify 8/(1+i) and write the complex number in standard form?

Jul 11, 2016

$4 - 4 i$

#### Explanation:

Recall that we can multiply the top and bottom of a fraction by the same thing without changing the value of the fraction. In this case we will multiply by the complex conjugate of the complex number on the denominator.

For $z = 1 + i$ we have $\overline{z} = 1 - i$

$\frac{8}{1 + i} \cdot \frac{1 - i}{1 - i} = \frac{8 - 8 i}{1 - {i}^{2}}$

Remember that ${i}^{2} = - 1$ so we have

$\frac{8 - 8 i}{2} = 4 - 4 i$