A complex number can be defined by quotiented polynomials
\mathbb{C} =\frac{\mathbb{R}[i]}{(i^2+1)\mathbb{R} [i]} $$ It can be viewed as adding a special value $i$ s.t. $i^2=-1$ They can be naturally represented in polar form: We define funcitions $\mathrm{Re},\mathrm{Im}:\mathbb{C}\rightarrow\mathbb{R}$ as\begin{aligned} \mathrm{Re}(a+bi)=a \ \mathrm{Re}(a+bi)=b \end{aligned}