[Cfp-interest 2742] Re: Definition of the 'carg' function

[Damian McGuckin]

On Thu, 30 Mar 2023, David Hough CFP wrote:

> It seems to me that old math books tend to use "modulus and argument"

I believe that the terms 'modulus' and 'argument' been around since 1805 
or so when used by Argand in his original work (treatise) in this whole 
subject.

> and new engineering books tend to use "magnitude and phase".  So if we 
> are aspiring to be modern engineers, we should use the latter.

Yes. Note that for this pair of terms,

    NIST's Digital Library of Mathemical Functions uses 'Modulus and Phase'

although it also uses 'magnitude' as an alternative to the first of these

Also, for the first of these terms, i.e. 'Modulus'

    ISO-80000-2-2009 uses "Absolute Value' or 'Modulus' or 'Magnitude'

as having equivalent standing.

I cannot find a published standard which uses magnitude as the predominent 
term, although there are published university lecture notes which do.

Now 'modulus' is one of the almost overloaded mathematical terms of all 
time. It has numerous meanings outside of complex numbers, e.g. in number 
theiry. And the concept of 'modulus' even differs in definition between 
different programming languages so it is a can of worms.

So all I can do is agree that I too like the term magnitude. That said, 
C23 already uses the words magnitude or modulus or norm as alternative 
names for absolute value of the complex number. Do we really want to make 
a change to this concept, especially when the function name is 'cabs', and 
for complex number 'z', we write

       cabs(z) = |z|

Food for thought follows ...

ISO-80000-2-2009 in 2.9.16 says

       |a|

can be

       absolute value of a
       modulus of a
       magnitude of a

independent of the type of 'a', i.e. it can be integral, real or complex. 
In 2.14.4 of that standard, it provides, for a complex 'a', the definition 
of |a| using the real and imaginary components of said complex 'a'.