Question 192529
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I suspect you used the correct process, but you have a little arithmetic problem.


The quadratic trinomial whose factors are <b><i>x</i> - (6 + 4<i>i</i>)</b> and <b><i>x</i> - (6 - 4<i>i</i>)</b> is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x - (6 + 4i)\right)\left(x - (6 - 4i)\right) = x^2 - (6 - 4i)x - (6 + 4i)x + (6 + 4i)(6 - 4i)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ = x^2 - 6x - 6x + 4ix - 4ix + (6^2 - (4i)^2) = x^2 - 12x + (36 - 16(-1)) = x^2 - 12x + 52]


Hence the desired equation is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 12x + 52 = 0]


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