How would you determine which method to use for simplifying a particular complex rational expression?

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For simplifying a complex rational expression we make use of copmlex conjugate( multiply and divide by the complex conjugate of the denominator).

e.g. In simplifying   (1-i)/(1+i).

The complex conjugate of the denominator (1+i) is (1-i)

 so  (1-i)*(1-i)/(1+i)*(1-i)=(1-i)^2/(1-i^2)

                                     =(1-2i+i^2)/(1-i^2)

                                     = (-2i)/2       as i^2=-1

                                     = -i. 

`1/(a+ib)=(a-ib)/{(a+ib).(a-ib)}`

` = (a-ib)/(a^2+b^2) `

`=a/(a^2+b^2)-i b/(a^2+b^2)`

`` means we multiply and devide by complex conjugate of the denomonator and simplify.

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