ABSTRACT
An operation upon complex numbers is a relation between two ordered pairs of real numbers and a third ordered pair, and it can be represented graphically on the complex plane. The sum (Sections 3.1 and 3.2) is most conveniently performed in the Cartesian representation, and the product (Sections 3.3 and 3.4) in the polar representation. The operations sum and product, and their inverses subtraction and division, can be used (Sections 3.5 and 3.6) together with the conjugate operator to determine the real and imaginary parts, and the modulus and argument, of complex expressions. The algebra of complex numbers is related to the geometry of the Cartesian plane (Sections 3.8 and 3.9), and implies a number of trigonometrical relations (Section 3.7). The algebra of complex numbers extends to functions of one or more variables, and thus to complex spaces whose real dimension is twice the number of complex variables.
