Complex Numbers and Exponentials

A complex number is nothing more than a point in the xy–plane. The first component, x, of the complex number (x, y) is called its real part and the second component, y, is called its imaginary part, even though there is nothing imaginary about it. The sum and product of two complex numbers (x1, y1) and (x2, y2) are defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) (x1, y1) (x2, y2) = (x1x2 − y1y2, x1y2 + x2y1)