# How do you rationalize  j/(1 - sqrt(j))?

May 13, 2015

Multiply and divide by $1 + \sqrt{j}$ to get:
$\frac{j}{1 - \sqrt{j}} \cdot \frac{1 + \sqrt{j}}{1 + \sqrt{j}} =$

You get:
$= \frac{j + j \sqrt{j}}{1 - j}$

$- - - - - - - - - - - - - - - - -$

If $j$ is considered as the imaginary unit: $j = \sqrt{- 1}$

You can divide by changing the denominator into a Real numbar as:

$\frac{j + j \sqrt{j}}{1 - j} \cdot \frac{1 + j}{1 + j} = \frac{j - 1 + j \sqrt{j} - \sqrt{j}}{2} = \frac{- 1 + j + \sqrt{j} \left[j - 1\right]}{2}$

Where ${j}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1$