Three forms, one number
There are three main ways of representing a complex number:
- Cartesian form (aka the general form)
- Polar form
- Exponential form
Each one has its advantages and disadvantages, depending on what we are trying to do. These will become evident as we go through them.
Definition of complex numbers
A complex number is a number that can be expressed in the following way:
(1)
where a and b are real numbers and i is the imaginary unit. The imaginary unit is defined as:
It follows from this that there are two square roots of -1, i and -i.
The real part of a complex number is denoted by Re(z) and the imaginary part is denoted by Im(z). For our complex number, z, defined in Equation (1), Re(z) = a and Im(z) = b. Two complex numbers, z and w, are equal if...
