User:Leapleap

$$ \begin{align} (a+bi)(c+di)&=(ac+adi+bci+bd(i^2)) \\ &=(ac-bd)+(ad + bc)i \\ &=(ac-bd)+((a + b)(c + d) - ac - bd)i \\ (a + b)(c + d) &= ac + ad + bc + bd \\ (a + b)(c + d) - ac - bd &= ad + bc \end{align} $$