# How do you simplify 2/(5-2i)?

Oct 22, 2016

the simplified form is $\frac{10}{29} + \frac{4 i}{29}$

#### Explanation:

To simplify, multiply the numerator and denominator by the conjugate of the denominator $5 + 2 i$

so $z = \frac{2}{5 + 2 i} = \frac{2 \left(5 + 2 i\right)}{\left(5 - 2 i\right) \left(5 + 2 i\right)} = \frac{10 + 4 i}{25 - 4 {i}^{2}}$

${i}^{2} = - 1$

So $z = \frac{10 + 4 i}{29} = \frac{10}{29} + \frac{4 i}{29}$