# How do you simplify (3+i)/(3-i) and write the complex number in standard form?

Jan 5, 2017

$\frac{4}{5} + i \frac{3}{5}$

#### Explanation:

Multiply the expression in the numerator and the denominator by the conjugate of the number in the denominator, to make the denominator a real number

$\frac{3 + i}{3 - i} \cdot \frac{3 + i}{3 + i}$

=$\frac{9 + 6 i + {i}^{2}}{9 - {i}^{2}}$

=$\frac{9 + 6 i - 1}{9 + 1}$

= $\frac{8 + 6 i}{10}$

=$\frac{8}{10} + \frac{6 i}{10}$

=$\frac{4}{5} + i \frac{3}{5}$