2. Terminology

The expression  for a complex number is called its polar form. The nonnegative real number r is called the absolute value or modulus or magnitude of P and we write r = |P|. The angle  is called an argument of P and is denoted as arg P.

A fixed point P always has a unique nonnegative real number r as its absolute value ( i.e., distance to O). On the other hand, P always has an infinite number of arguments since

For example, some of the other representations for the point  of Figure 1a are  Also,  are several of the representations of U.

The set of points in the Argand Plane is made into the Complex Number System by defining addition and multiplication as follows:

Sum. P + Q is the point S such that the directed segment  has the same magnitude and direction as  This means that the equation S = P + Q implies that the quadrilateral OPSQ is a parallelogram (See Figure 2) unless it collapses into a line segment.	Figure 2
Product. If  then Thus PQ is the point whose absolute value is the product of the absolute values of P and Q and whose arguments are the sums of an argument of P and an argument of Q. This is consistent with the fact that the angles  appear in the exponents. See Figure 3.	Figure 3