View source for HW1.3 Josh Long - Complex Modulus (Norms) ECE301Fall2008mboutin - Rhea

[[Category:Complex Number Magnitude]]
[[Category:ECE301]]

== Complex Modulus  ([[Homework_1_ECE301Fall2008mboutin|HW1]], [[ECE301]], [[Main_Page_ECE301Fall2008mboutin|Fall 2008]])==
Complex Modulus, also known as the "Norm" of a complex number, is represented as <math>|z|</math>.

<math>|x + iy| = \sqrt{x^2 + y^2}</math>


In exponential form for <math>|z|</math> 

<math>|re^{i\phi}| = r</math>

(This format is used when dealing with Phasors)

== Basics ==

*<math>\frac{|Ae^{i\phi_{1}}|}{|Be^{i\phi_{2}}|} = \frac{A}{B}\frac{|e^{i\phi_{1}}|}{|e^{i\phi_{2}}|} = \frac{A}{B}</math>


*<math>|\frac{Ae^{i\phi_{1}}}{Be^{i\phi_{2}}}| = \frac{A}{B}|e^{i(\phi_{1}-\phi_{2})}| = \frac{A}{B}</math>


*<math>|\frac{Ae^{i\phi_{1}}}{Be^{i\phi_{2}}}| = \frac{|Ae^{i\phi_{1}}|}{|Be^{i\phi_{2}}|}</math>


*<math>|Ae^{i\phi_{1}}||Be^{i\phi_{2}}| = {A}{B}|e^{i\phi_{1}}||e^{i\phi_{2}}| = {A}{B}</math>


*<math>|(Ae^{i\phi_{1}})(Be^{i\phi_{2}})| = {A}{B}|e^{i\phi_{1}+i\phi_{2}}| = {A}{B}</math>


*<math>|Ae^{i\phi_{1}}||Be^{i\phi_{2}}| = |(Ae^{i\phi_{1}})(Be^{i\phi_{2}})|</math>


*<math>|z^n|=|z|^n</math>


*<math>|z|^2</math> of <math>|z|</math> is known as the '''Absolute Square'''.


*<math>z\overline z=|z|^2</math>

      Where <math>z</math> is a complex number and <math>\overline z</math> is the complex conjugate.
      
      <math>z = x + iy</math>
      
      <math>\overline z=x-iy</math>
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