Notation

For differing or unknown values of the complex number, for instance the "H" that was used to represent the hypotenuse, a standard set of characters are used as illustrated in the diagram below;

As you can readily see, this means that  "c = a +jb" there are other notations used, for instance in electrical engineering, values of impedance et cetera are depicted as z for the hypotenuse. More on that later.

Argand diagram

consider the following diagram

Here are plotted four phasors with their respective Cartesian complex number values. The diagram for showing these numbers is called an Argand diagram. Named after, but not invented by, Jean Robert Argand. It was, in fact, invented some years earlier by Casper Wessel.

Polar Form

The polar form is simply another way of expressing a complex number. We have already discussed the fact that a complex number has both magnitude and direction. We can express this by giving not only the real and imaginary values, but by giving the magnitude (length) of the hypotenuse, called the modulus, with respect to the angle between it and the real axis. The angle is referred to as the argument between the modulus and the real axis. Think about it. The diagram below illustrates the modulus and the argument.

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