\(\def\Real{\mathbb{R}}\def\Comp{\mathbb{C}}\def\Rat{\mathbb{Q}}\def\Field{\mathbb{F}}\def\Fun{\mathbf{Fun}}\def\e{\mathbf{e}}\def\f{\mathbf{f}}\def\bv{\mathbf{v}}\def\i{\mathbf{i}}

\def\eye{\left(\begin{array}{cc}1&0\\0&1\end{array}\right)}

\)

Complex numbers are expressions \(z=x+\i y\), where \(\i\) is the *imaginary unit*, defined by \(\i^2=-1\). Note the ambiguity (\(-\i\) would work just as well).

Complex numbers can be added subtracted, multiplied the usual way, with the …