IEC 60050 - International Electrotechnical Vocabulary


IEVref:	102-02-17		ID:
Language:	en		Status: Obsolete

Term:	argument (of a complex number)
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Symbol:
Definition:	for a non-zero complex number c, the real number φ restricted to $- π < φ \leq π$ , such that $c = \| c \| e^{j φ}$ NOTE 1 The argument $\arg c$ of the complex number $c = a + j b = \| c \| e^{j φ}$ is equal to: $\arccos (a / \sqrt{a^{2} + b^{2}})$ if $b \geq 0$ and $- \arccos (a / \sqrt{a^{2} + b^{2}})$ if $b < 0$ , where $0 \leq \arccos x \leq π$ . It is not defined if $a = b = 0$ . NOTE 2 The concept of argument may be applied to complex scalar quantities.
Publication date:	2007-08
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Internal notes:	2017-06-02: Cleanup - Remove Attached Image 102-02-17en.gif
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cφ −π<φ≤π MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiabgkHiTGWaaiab=b 8aWjabgYda8iabew9aMjabgsMiJkab=b8aWbaa@41B6@ c=|c| e jφ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadogacqGH9aqpda abdaqaaiaadogaaiaawEa7caGLiWoajugqbiaacwgakmaaCaaaleqa baGaaiOAaiabew9aMbaaaaa@434A@ NOTE 1 The argument

\arg c

of the complex number

c = a + j b = | c | e^{j φ}

is equal to:

\arccos (a / \sqrt{a^{2} + b^{2}})

if

b \geq 0

and

- \arccos (a / \sqrt{a^{2} + b^{2}})

if

b < 0

, where

0 \leq \arccos x \leq π

.
It is not defined if

a = b = 0

. NOTE 2 The concept of argument may be applied to complex scalar quantities.