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 (x − a)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 ...