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

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Answer 1 · 2015-05-13T16:14:26

Multiply and divide by #1+sqrt(j)# to get:
#j/(1-sqrt(j))*(1+sqrt(j))/(1+sqrt(j))=#

You get:
#=(j+jsqrt(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:

#(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#