evaluation of complex fractionhow to evaluate a complex fraction?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The request of the problem is vague since it is not clear what is needed, hence, supposing that you need to work with a fraction that has a complex number to dennominator, you need to perform first a multiplication to both, numerator and denominator, with the conjugate of the complex number, such that:

`1/(x + i*y) = (x - i*y)/((x + i*y)(x - i*y))`

You need to convert the product to denominator into a difference of squares, such that:

`1/(x + i*y) = (x - i*y)/(x^2 - y^2*i^2)`

`1/(x + i*y) = (x - i*y)/(x^2 - y^2*(-1))`

`1/(x + i*y) = (x - i*y)/(x^2 + y^2)`

Hence, when the fraction has a complex number to denominator, you need to multiply by its conjugate to transform the complex denominator into a real denomminator.