Question 199782
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If *[tex \Large \alpha] and *[tex \Large \beta] are roots of the equation *[tex \Large ax^2 + bx + c = 0], then *[tex \Large x - \alpha] and *[tex \Large x - \beta] are factors of the trinomial *[tex \Large ax^2 + bx + c].


So the product of:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x - (1 + i)\right)\left(x - (1 - i)\right)]


will result in the desired monic univariate polynomial.


<b><u>Hints:</u></b>


1.  Treat *[tex \Large 1 + i] and *[tex \Large 1 - i] as single numbers and apply FOIL.


2.  *[tex \Large (1 + i)(1 - i)] results in the difference of two squares.


3.  Remember that *[tex \Large i^2 = -1]


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