How do you rationalize j/(1 - sqrt(j))j1−√j?

1 Answer
Gió
May 13, 2015

Multiply and divide by 1+sqrt(j)1+√j to get:
j/(1-sqrt(j))*(1+sqrt(j))/(1+sqrt(j))=j1−√j⋅1+√j1+√j=

You get:
=(j+jsqrt(j))/(1-j)=j+j√j1−j

-----------------−−−−−−−−−−−−−−−−−

If jj is considered as the imaginary unit: j=sqrt(-1)j=√−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])/2j+j√j1−j⋅1+j1+j=j−1+j√j−√j2=−1+j+√j[j−1]2

Where j^2=(sqrt(-1))^2=-1j2=(√−1)2=−1

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