Question

What is a complex conjugate?

Answer 1

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`).