# Complex number

The set $\mathbb{C}$ of complex numbers is defined by $$\mathbb{C} = \left\{ a+bi \colon a,b \in \mathbb{R} \right\},$$ where $i=\sqrt{-1}$ is the imaginary number and $\mathbb{R}$ is the set of real numbers. The set $\mathbb{C}$ imbued with the natural addition and multiplication operations inherited from $\mathbb{R}$ is an algebraically closed field.