Absolute Square
المؤلف:
المرجع الالكتروني للمعلوماتيه
المصدر:
المرجع الالكتروني للمعلوماتيه
الجزء والصفحة:
...
18-10-2018
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Absolute Square
The absolute square of a complex number 
, also known as the squared norm, is defined as
 |
(1)
|
where 
denotes the complex conjugate of 
and 
is the complex modulus.
If the complex number is written 
, with 
and 
real, then the absolute square can be written
 |
(2)
|
If 
is a real number, then (1) simplifies to
 |
(3)
|
An absolute square can be computed in terms of 
and 
using the Wolfram Language command ComplexExpand[Abs[z]^2, TargetFunctions -> ![<span style=]()
{" src="http://mathworld.wolfram.com/images/equations/AbsoluteSquare/Inline11.gif" style="height:14px; width:5px" />Conjugate![<span style=]()
}" src="http://mathworld.wolfram.com/images/equations/AbsoluteSquare/Inline12.gif" style="height:14px; width:5px" />].
An important identity involving the absolute square is given by
If 
, then (6) becomes
If 
, and 
, then
 |
(9)
|
Finally,
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