Editing Difference of two squares (section)

===Complex number case: sum of two squares===
The difference of two squares is used to find the [[linear factors]] of the ''sum'' of two squares, using [[complex number]] coefficients.

For example, the complex roots of <math>z^2 + 4</math> can be found using difference of two squares:

<math display=block>\begin{align}
z^2 + 4 &= z^2 - 4i^2 \\
&= z^2 - (2 i)^2 \\
&= (z + 2 i)(z - 2 i). \\
\end{align}</math>

Therefore, the linear factors are <math>(z + 2 i)</math> and <math>(z - 2 i)</math>.

Since the two factors found by this method are [[complex conjugate]]s, we can use this in reverse as a method of multiplying a complex number to get a real number. This is used to get real denominators in complex fractions.<ref>[http://www.themathpage.com/alg/complex-numbers.htm#conjugates Complex or imaginary numbers] TheMathPage.com, retrieved 22 December 2011</ref>