\begin{definition}[Definition:Complex Conjugate]
Let $z = a + i b$ be a complex number.
Then the '''(complex) conjugate''' of $z$ is denoted $\overline z$ and is defined as:
:$\overline z := a - i b$
That is, you get the '''complex conjugate''' of a complex number by negating its imaginary part.
\end{definition}