Complex-Numbers

Complex-Numbers - Complex Numbers Introduction If we try to...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Complex Numbers Introduction If we try to solve x 2 = -1, what happens? We extract square roots to get x = +/- -1. But if we try to evaluate the square root of –1 on a scientific calculator, we get ERROR! But still, we need a way to define solutions like this so it is defined that i 2 = -1 and thus i = (-1). This means that the solutions of x 2 = -1 are x = i and x = -i We refer to such solutions as Complex Solutions . Furthermore, we refer to a number containing the quantity “i”, where i = -1, as an imaginary number . This choice of words “imaginary” is actually not appropriate, since we use the number “i” in many real-world engineering applications! Using Complex Numbers To Evaluate Square Roots Given that i 2 = -1 and thus i = (-1), we can use this fact to evaluate any square root. For example, (-13) = (-1 13) = (-1) 13 and we can replace (-1) with i to get (-13) = i •√ 13. In general, we can say that
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Complex-Numbers - Complex Numbers Introduction If we try to...

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