(New page: == Magnitude of a Complex Number == Complex numbers include real numbers as well as the imaginary number j, which represents the squareroot of negative one ...) |
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| − | == Magnitude of a Complex Number == | + | [[Category:Complex Number Magnitude]] |
| + | [[Category:ECE301]] | ||
| + | == Magnitude of a Complex Number ([[Homework_1_ECE301Fall2008mboutin|HW1]], [[ECE301]], [[Main_Page_ECE301Fall2008mboutin|Fall 2008]])== | ||
| − | Complex numbers include real numbers as well as the imaginary number j, which represents the | + | Complex numbers include real numbers as well as the imaginary number j, which represents <math class="inline">\sqrt{-1}</math>. |
| + | |||
| + | Complex numbers are harder to deal with than real numbers because of the two parts they contain, real and imaginary. Simple operations like finding the absolute value (aka. Magnitude or Norm) are more difficult. | ||
| + | |||
| + | Magnitude |z| of complex number z is | ||
| + | |||
| + | <math > |z| = \sqrt{Re(z)^2 + Im(z)^2}</math> | ||
| + | ---- | ||
| + | <span style="color:red"> One comment on the term "absolute value": there is no such thing as the "absolute value of a complex number". One can only talk about the absolute value of a real number: the absolute value of a real number corresponds to the magnitude (or norm) of that number. | ||
| + | If you write on your exam that the magnitude (or norm) of a complex number is given by its absolute value, then technically this is incorrect and points could be taken off. -pm </span> | ||
| + | ---- | ||
| + | [[Main_Page_ECE301Fall2008mboutin|Back to ECE301 Fall 2008 Prof. Boutin]] | ||
| + | |||
| + | [[ECE301|Back to ECE301]] | ||
| + | |||
| + | [[More_on_complex_magnitude|Back to Complex Magnitude page]] | ||
| + | |||
| + | Visit the [[ComplexNumberFormulas|"Complex Number Identities and Formulas" page]] | ||
Latest revision as of 05:35, 23 September 2011
Magnitude of a Complex Number (HW1, ECE301, Fall 2008)
Complex numbers include real numbers as well as the imaginary number j, which represents $ \sqrt{-1} $.
Complex numbers are harder to deal with than real numbers because of the two parts they contain, real and imaginary. Simple operations like finding the absolute value (aka. Magnitude or Norm) are more difficult.
Magnitude |z| of complex number z is
$ |z| = \sqrt{Re(z)^2 + Im(z)^2} $
One comment on the term "absolute value": there is no such thing as the "absolute value of a complex number". One can only talk about the absolute value of a real number: the absolute value of a real number corresponds to the magnitude (or norm) of that number. If you write on your exam that the magnitude (or norm) of a complex number is given by its absolute value, then technically this is incorrect and points could be taken off. -pm
Back to ECE301 Fall 2008 Prof. Boutin
