# What is a complex conjugate?

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 $\left(a + b i\right) . \left(c + \mathrm{di}\right)$ is real, ($c + \mathrm{di}$) is ($a + b i$)'s conjugate and it equals ($a - b i$).