# Definition
$\mathbb{C}$ is obtained from $\mathbb{R}$ by adjoining the imaginary unit $i$ such that $i^2 = -1$.

In particular, a complex number is of the form
$$z = x+iy$$
with $x$, $y$ being real, we write
$$\mathrm{Re} z = x, \; \mathrm{Im} z = y.$$
# Absolute Value
Let $z = x+iy$. Its **absolute value** (or [[Norm|norm]]) is defined by 
$$\mid z \mid \sqrt{ x^2 + y^2 }.$$