• Multiplication, Reciprocal & Division
For 2 dimensional numbers,
x = [p∠φ] = [p·→φ,p·↑φ] = [a,b]
y = [q∠ψ] = [q·→ψ,q·↑ψ] = [c,d]
Multiplication x·y = [(p·q)∠(φ+ψ)]
= [(p·q)·→(φ+ψ),(p·q)·↑(φ+ψ)]
= [p·q·(→φ·→ψ−↑φ·↑ψ), p·q·(↑φ·→ψ+→φ·↑ψ)]
= [p·→φ·q·→ψ−p·↑φ·q·↑ψ, p·↑φ·q·→ψ+p·→φ·q·↑ψ]
= [a·c−b·d, ...
http://qindex.info/i.php?x=9628
