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) is defined by

\mid z \mid \sqrt{ x^2 + y^2 }.