How do you rationalize $\frac{j}{1 - \sqrt{j}}$ $j/(1 - sqrt(j))$ ?

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How do you rationalize $\frac{j}{1 - \sqrt{j}}$ $j/(1 - sqrt(j))$ ?

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Answer 1 · 2015-05-13T16:14:26

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

You get:
$= \frac{j + j \sqrt{j}}{1 - j}$ $=(j+jsqrt(j))/(1-j)$

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

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

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

$\frac{j + j \sqrt{j}}{1 - j} \cdot \frac{1 + j}{1 + j} = \frac{j - 1 + j \sqrt{j} - \sqrt{j}}{2} = \frac{- 1 + j + \sqrt{j} [j - 1]}{2}$ $(j+jsqrt(j))/(1-j)*(1+j)/(1+j)=(j-1+jsqrt(j)-sqrt(j))/2=(-1+j+sqrt(j)[j-1])/2$

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

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How do you rationalize $\frac{j}{1 - \sqrt{j}}$ $j/(1 - sqrt(j))$ ?

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