# How do you write ((5-2i)+(5+3i))/((1+i)-(2-4i)) in standard form?

Feb 18, 2017

$- \frac{5}{26} - \frac{51}{26} i$

#### Explanation:

Add like terms in the numerator and denominator:
$\frac{\left(5 + 5\right) + \left(- 2 i + 3 i\right)}{\left(1 + - 2\right) + \left(i - - 4 i\right)} = \frac{10 + i}{- 1 + 5 i}$

Multiple by $1$ using the conjugate of the denominator:
:$\frac{10 + i}{- 1 + 5 i} \cdot \frac{- 1 - 5 i}{- 1 - 5 i} = \frac{- 10 - 50 i - i - 5 {i}^{2}}{1 - 25 {i}^{2}}$

Remember that ${i}^{2} = - 1$:

$\frac{- 10 - 50 i - i + 5}{1 + 25} = \frac{- 5 - 51 i}{26}$

Put in standard form: $- \frac{5}{26} - \frac{51}{26} i$