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The Calculus Lifesaver by Adrian Banner

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CHAPTER 28 _____________________________

Complex Numbers

Why should some quadratics have all the fun? The quadratic x2 − 1 gets the privilege of having two roots (1 and − 1), but poor old x2 + 1 doesn’t have any, since its discriminant is negative. To even things up a little, let’s introduce the concept of complex numbers. Using complex numbers, any quadratic has two roots.* (You have to count the double root a of (xa)2 as two roots.) Anyway, here’s what we’re going to be doing with complex numbers:

• basic manipulations (adding, subtracting, multiplying, dividing) and solving quadratic equations;

• the complex plane, and Cartesian and polar forms for complex numbers;

• taking large powers of complex numbers;

• solving equations of the form ...

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