Complex Modulus
Complex Modulus, also known as the "Norm" of a complex number, is represented as $ |z| $.
$ |x + iy| = \sqrt{x^2 + y^2} $
In exponential form for $ |z| $
$ |re^{i\phi}| = r $
(This format is used when dealing with Phasors)
Basics
- $ |z|^2 $ of $ |z| $ is known as the Absolute Square.
- $ \frac{|Ae^{i\phi}|}{|Be^{i\phi}|} = \frac{A}{B}\frac{|e^{i\phi}|}{|e^{i\phi}|} = \frac{A}{B} $
- $ |\frac{Ae^{i\phi}}{Be^{i\phi}}| = \frac{A}{B}|e^{i(\phi-\phi)}| = \frac{A}{B} $
- $ |\frac{Ae^{i\phi}}{Be^{i\phi}}| = \frac{|Ae^{i\phi}|}{|Be^{i\phi}|} $
