complex modulus - Wolfram|Alpha

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Input interpretation

complex modulus

Alternate name

complex norm

Definition

The modulus of a complex number z, also called the complex norm, is denoted left bracketing bar z right bracketing bar and defined by
left bracketing bar x + i y right bracketing bar congruent sqrt(x^2 + y^2).
If z is expressed as a complex exponential (i.e., a phasor), then
left bracketing bar r e^(i ϕ) right bracketing bar = left bracketing bar r right bracketing bar .
The complex modulus is implemented in the Wolfram Language as Abs[z], or as Norm[z].
The square ( left bracketing bar z right bracketing bar )^2 of left bracketing bar z right bracketing bar is sometimes called the absolute square.
Let c_1 congruent A e^(i ϕ_1) and c_2 congruent B e^(i ϕ_2) be two complex numbers.

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Related terms

absolute square | absolute value | complex argument | complex number | imaginary part | maximum modulus principle | minimum modulus principle | real part

Related Wolfram Language symbols

Abs | Norm

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