# How do you simplify (8+10i)/(8+6i) and write in a+bi form?

Mar 12, 2018

$\frac{31 + 8 i}{21}$

#### Explanation:

Multiply the numerator and denominator by the conjugate of the denominator :

$\frac{8 + 10 i}{8 + 6 i} = \frac{\left(8 + 10 i\right) \times \left(8 - 6 i\right)}{\left(8 + 6 i\right) \times \left(8 - 6 i\right)}$

$= \frac{64 - 48 i + 80 i - 60 {i}^{2}}{64 - 36 {i}^{2}}$

=(64+60(-i^2)−48i+80i)/(64+36(-i^2))

$\frac{124 + 32 i}{100}$

simplifiying:

$\frac{31 + 8 i}{25}$