# How do you simplify (2i)/(1-i) and write the complex number in standard form?

Jul 3, 2016

$= - 1 + i$

#### Explanation:

multilply by the conjugate of the denominator

that gives you

$\frac{2 i}{1 - i} \cdot \frac{1 + i}{1 + i}$

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

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

$= - 1 + i$