I found the following link:
They have shown something like that:
(a + bi)(c + di) = ac − bd + (bc + ad)i-----(1) =ac − bd + (bc + ad)i =bc + ad = (a + b)(c + d) − ac – bd
In the above I can't understand how there are 3 multiplications because if we put the values back in (1), we would get something like:
=ac -bd + [(a+b)(c+d) -ac -bd]i
Above looks like 5 multiplications:
I tried to go further:
= ac -bd -aci -bdi + (a+b)(c+d)i =ac(1-i) -bd(1 + i) +(a+b)(c+d)i
I don't know if the above is correct to show that there are 3 multiplications.
Somebody please guide me.