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Complex Numbers in Matlab and Octave

Matlab and Octave have the following primitives for complex numbers:

octave:1> help j

j is a built-in constant
 
 - Built-in Variable: I
 - Built-in Variable: J
 - Built-in Variable: i
 - Built-in Variable: j

A pure imaginary number, defined as `sqrt (-1)'.  The `I' and `J'
forms are true constants, and cannot be modified.  The `i' and `j'
forms are like ordinary variables, and may be used for other
purposes.  However, unlike other variables, they once again assume
their special predefined values if they are cleared *Note Status
of Variables::.

Additional help for built-in functions, operators, and variables
is available in the on-line version of the manual.  Use the command
`help -i <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the help-octave@bevo.che.wisc.edu
mailing list.

octave:2> sqrt(-1)
ans = 0 + 1i

octave:3> help real
real is a built-in mapper function

 - Mapping Function:  real (Z)
     Return the real part of Z.

See also: imag and conj. ...

octave:4> help imag
imag is a built-in mapper function

 - Mapping Function:  imag (Z)
     Return the imaginary part of Z as a real number.

See also: real and conj. ...

octave:5> help conj
conj is a built-in mapper function

 - Mapping Function:  conj (Z)
     Return the complex conjugate of Z, defined as 
     `conj (Z)' = X - IY.

See also: real and imag. ...

octave:6> help abs
abs is a built-in mapper function

 - Mapping Function:  abs (Z)
     Compute the magnitude of Z, defined as 
     |Z| = `sqrt (x^2 + y^2)'.

     For example,

          abs (3 + 4i)
          => 5
...
octave:7> help angle
angle is a built-in mapper function

 - Mapping Function:  angle (Z)
     See arg.
...
Note how helpful the ``See also'' information is in Octave (and similarly in Matlab).



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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-10-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA