What is a complex conjugate?

1 Answer

A complex conjugate is the number to which you have to multiply a complex number in order to make it real.
By using the identity #(x+y) . (x-y) = x²-y²#, we see that, to every complex, there is another to which we can multiply it in order to get a new number that will not depend on #i#.
If #(a+bi).(c+di)# is real, (#c+di#) is (#a+bi#)'s conjugate and it equals (#a-bi#).