## Complex Modulus (HW1, ECE301, Fall 2008)

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

• $\frac{|Ae^{i\phi_{1}}|}{|Be^{i\phi_{2}}|} = \frac{A}{B}\frac{|e^{i\phi_{1}}|}{|e^{i\phi_{2}}|} = \frac{A}{B}$

• $|\frac{Ae^{i\phi_{1}}}{Be^{i\phi_{2}}}| = \frac{A}{B}|e^{i(\phi_{1}-\phi_{2})}| = \frac{A}{B}$

• $|\frac{Ae^{i\phi_{1}}}{Be^{i\phi_{2}}}| = \frac{|Ae^{i\phi_{1}}|}{|Be^{i\phi_{2}}|}$

• $|Ae^{i\phi_{1}}||Be^{i\phi_{2}}| = {A}{B}|e^{i\phi_{1}}||e^{i\phi_{2}}| = {A}{B}$

• $|(Ae^{i\phi_{1}})(Be^{i\phi_{2}})| = {A}{B}|e^{i\phi_{1}+i\phi_{2}}| = {A}{B}$

• $|Ae^{i\phi_{1}}||Be^{i\phi_{2}}| = |(Ae^{i\phi_{1}})(Be^{i\phi_{2}})|$

• $|z^n|=|z|^n$

• $|z|^2$ of $|z|$ is known as the Absolute Square.

• $z\overline z=|z|^2$
     Where $z$ is a complex number and $\overline z$ is the complex conjugate.

$z = x + iy$

$\overline z=x-iy$


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