Question 324399
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t^2] means multiply *[tex \LARGE t\ \times\ t]


So if 12.5 is the answer, that means that *[tex \LARGE 12.5\ \times\ 12.5\ =\ 25]


Get out the calculator.  12.5, X, =.  Calculator says 156.25.  Not 25.


You want the number when multiplied by itself is equal to *[tex \LARGE t].  BUT don't stop there.  Once you recall from your 3rd grade multiplication tables which number times itself equals 25 you only have half the answer.  That is because a positive number times a positive number is a positive number, but a negative number times a negative number is ALSO a positive number.  That means both the positive and the negative of the value are answers to this problem.  


The fact that this problem has two answers makes good sense -- the Fundamental Theorem of Algebra says that a non-zero polynomial equation with complex coefficients has as many roots, counting multiplicities, as the degree of the polynomial. You have a polynomial of degree 2, so there has to be two roots.


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