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 > Conjugate].
An important identity involving the absolute square is given by
(4)
 
(5)
 
(6)

If , then (6) becomes
(7)
 
(8)

If , and , then
(9)

Finally,
(10)
 
(11)
 
(12)
