Conjugate

Say

z=a+biz=a+bi

Let the conjugate z∗z^* of zz be defined as this (we just make the imaginary part negative)

z∗=a−bi=(a+b−ba)\begin{gather*} z^*=a-bi=\begin{pmatrix}a & +b \\ -b & a \end{pmatrix} \end{gather*}

If you’re writing in Euler Form, then flip the sign of the angle

(eiθ)∗=e−iθ(e^{i\theta})^*=e^{-i\theta}