Question 584346
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-1\,+\,3i}{1\,+\,i}]


Multiply the fraction by 1 in the form of the conjugate of the denominator divided by itself:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{-1\,+\,3i}{1\,+\,i}\right)\left(\frac{1\,-\,i}{1\,-\,i}\right)]


Use FOIL for the numerator and the fact that the product of a pair of binomial conjugates is the difference of two squares for the denominator.  Don't forget that *[tex \LARGE i^2\ =\ -1]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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