# How do you divide (2i) / (1 - i)?

Jan 21, 2016

1 - i

#### Explanation:

Multiply numerator and denominator by the complex conjugate
of (1 - i ) which is ( 1 + i ). This ensures the denominator is real.

(Remember that :  i^2 = - 1)

$\frac{2 i \left(1 + i\right)}{\left(1 - i\right) \left(1 + i\right)}$

( multiply out brackets- distribute )

= $\frac{2 i + 2 {i}^{2}}{1 - {i}^{2}} = \frac{2 i - 2}{2} = \frac{\cancel{2} \left(1 - i\right)}{\cancel{2}}$

$\Rightarrow \frac{2 i}{1 - i} = 1 - i$