Complex Number Modulus

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A Complex Number Modulus is a norm of the complex number in the complex plane.



References

2015

[math]\displaystyle{ |z| = \sqrt{x^2 + y^2}. }[/math]
When the imaginary part [math]\displaystyle{ y }[/math] is zero this is the same as the absolute value of the real number [math]\displaystyle{ x }[/math]
When a complex number [math]\displaystyle{ z }[/math] is expressed in polar form as [math]\displaystyle{ z = r e^{i \theta} }[/math] with [math]\displaystyle{ r \geq 0 }[/math] and [math]\displaystyle{ \theta }[/math] real, its absolute value is [math]\displaystyle{ |z| = r }[/math].


1999

[math]\displaystyle{ |x+iy|=\sqrt{x^2+y^2} }[/math]
If [math]\displaystyle{ z }[/math] is expressed as a complex exponential (i.e., a phasor), then
[math]\displaystyle{ |re^{i\phi}|=|r| }[/math]