# How do you write ((10+4i)-(3-2i))/((6-7i)(1-2i)) in standard form?

Apr 21, 2018

$\frac{10 + 4 i - \left(3 - 2 i\right)}{\left(6 - 7 i\right) \left(1 - 2 i\right)} = - \frac{2}{5} + \frac{i}{5}$

#### Explanation:

$\frac{10 + 4 i - \left(3 - 2 i\right)}{\left(6 - 7 i\right) \left(1 - 2 i\right)}$

Simplify numerator and multiply out denominator

$\frac{7 + 6 i}{- 8 - 19 i}$

Multiply the numerator and denominator by the complex conjugate of the denominator.

$\frac{\left(7 + 6 i\right) \left(- 8 + 19 i\right)}{\left(- 8 - 19 i\right) \left(- 8 + 19 i\right)}$

Apply the distributive property to the numerator and denominator.

$\frac{- 170 + 85 i}{425}$

Factor out the common factor.

$\frac{85 \left(- 2 + i\right)}{85 \left(5\right)}$

Simplify.

$\frac{- 2 + i}{5} = - \frac{2}{5} + \frac{i}{5}$