Question 252055
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FOIL the numerator and denominator remembering that *[tex \LARGE i^2\ =\ -1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(3\,+\,2i)(6\,-\,i)}{(2\,+\,i)(4\,+\,2i)}\ =\ \frac{20\,+\,9i}{6\,+\,8i}]


Form the conjugate of the denominator, that is change the sign in the middle, *[tex \LARGE 6\,-\,8i].


Multiply your fraction by 1 in the form of the conjugate of the denominator divided by itself.  Note the difference of two squares result in the denominator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{20\,+\,9i}{6\,+\,8i}\ =\ \left(\frac{20\,+\,9i}{6\,+\,8i}\right)\left(\frac{6\,-\,8i}{6\,-\,8i}\right)\ =\ \frac{192\,-\,106i}{36\,-\,(-64)}\ =\ \frac{192\,-\,106i}{100}\ =\ 1.92\,-\,1.06i]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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