How do you write the following expression in standard form 2/(1+i)-3/(1-i)?

Feb 9, 2017

$\frac{2}{1 + i} - \frac{3}{1 - i} = - \frac{1}{2} - \frac{5}{2} i$

Explanation:

We combine the two fractions with a common denominator, and simplify:

$\frac{2}{1 + i} - \frac{3}{1 - i} = \frac{2 \left(1 - i\right) - 3 \left(1 + i\right)}{\left(1 + i\right) \left(1 - i\right)}$
$\text{ } = \frac{2 - 2 i - 3 - 3 i}{1 + i - i - {i}^{2}}$
$\text{ } = \frac{- 1 - 5 i}{1 - {i}^{2}}$
$\text{ } = \frac{- 1 - 5 i}{1 + 1} \setminus \setminus \setminus \setminus \setminus \left(\because {i}^{2} = - 1\right)$
$\text{ } = \frac{- 1 - 5 i}{2}$
$\text{ } = - \frac{1}{2} - \frac{5}{2} i$