# How do you simplify (2+5i)/ (1-i)?

Jan 11, 2016

$\frac{2 + 5 i}{1 - i} = - \frac{3}{2} + \frac{7}{2} i$

#### Explanation:

The conjugate of a complex number $a + b i$ is $a - b i$. The product of a complex number and its conjugate is a real number. We will use this fact to produce a real number in the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

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

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

$= \frac{- 3 + 7 i}{2}$

$= - \frac{3}{2} + \frac{7}{2} i$