If we break up a complex number into its two components we can make a new plot. Let the imaginary part be the y-axis and let the real part be the y-axis.
We can write the complex number z in terms of a (real part), b (imaginary part), r (the hypotenuse from the origin to Z), and theta (radians from the x-axis to r):
- a+jb Rectangular Form
- re^(j*theta) Polar Form
Next we discussed Euler's Equality: e^(j*theta) = cos(theta) + j*sin(theta) use to convert from polar form to rectangular form
Therefore when we set theta to pi (cosine is -1 and sine is 0), e^j*pi = -1
