for z being Quaternion holds z ^2 = [*(((((Rea z) ^2) - ((Im1 z) ^2)) - ((Im2 z) ^2)) - ((Im3 z) ^2)),(2 * ((Rea z) * (Im1 z))),(2 * ((Rea z) * (Im2 z))),(2 * ((Rea z) * (Im3 z)))*]