We define one more operation with complex numbers that may be new to you.
The modulus of the complex number $\alpha=a+bi\in\complex{\null}$, is the nonnegative real number \begin{equation*} \modulus{\alpha}=\sqrt{\conjugate{\alpha}\alpha}=\sqrt{a^2+b^2}. \end{equation*}
The modulus can be interpreted as a version of the absolute value for complex numbers, as is suggested by the notation employed. You can see this in how $\modulus{-3}=\modulus{-3+0i}=3$. Notice too how the modulus of the complex zero, $0+0i$, has value $0$.