Is there a name for this formula?
- Thread starter magic
- Start date
Hello, magic!
I don't recall a name for this identity,
. . but it is even more fascinating . . .
Given a sum-of-two-squares, \(\displaystyle a^2+b^2\), and another, \(\displaystyle c^2+d^2\),
. . their product can be expressed as a sum-of-two-squares in two ways.
. . \(\displaystyle (a^2+b^2)(c^2+d^2) \;=\;\begin{Bmatrix}(ac+bd)^2 + (ad-bc)^2 \\ \\ (ac-bd)^2 + (ad+bc)^2\end{Bmatrix}\)
I don't recall a name for this identity,
. . but it is even more fascinating . . .
Given a sum-of-two-squares, \(\displaystyle a^2+b^2\), and another, \(\displaystyle c^2+d^2\),
. . their product can be expressed as a sum-of-two-squares in two ways.
. . \(\displaystyle (a^2+b^2)(c^2+d^2) \;=\;\begin{Bmatrix}(ac+bd)^2 + (ad-bc)^2 \\ \\ (ac-bd)^2 + (ad+bc)^2\end{Bmatrix}\)
NIce
Do you know if it covers the complete solution set for \(\displaystyle a^2+b^2=c^2+d^2\) ?
Thanks