Representing Complex Numbers
Recall that one source of complex numbers comes from solving quadratic equations that result in trying to take the square root of a negative number.
These are the type of graphs that never touch the x-axis.
Complex numbers can't be graphed on a normal (x,y) plane because of the imaginary component (the 'bi'), but they can be graphed if we rename the x,y axis to Real and Imaginary:
![Picture](/uploads/3/7/4/1/37417637/2988084.png?439)
Note that the imaginary component is represented as 2j instead of 2i. This is because there is an ongoing issue between mathematics and electrical engineering. Math used i to represent the √-1. Electrical engineers use i to represent current. So, electrical engineers use i to represent current and j to represent √-1.
Expressing complex numbers in polar form is nothing more than finding the magnitude of the vector (hypotenuse) and the reference angle theta.