Argand Plane

algebra complex-numbers

Definition

Argand Plane

The Argand plane (also called the complex plane or Gaussian plane) is the geometric representation of $\mathbb{C}$ as ${\mathbb{R}}^2$, where a complex number $z=x+iy$ is identified with the point $(x,y)$.

The horizontal axis is the real axis $\Re$ and the vertical axis is the imaginary axis $\Im$.

Addition in $\mathbb{C}$ corresponds to vector addition in ${\mathbb{R}}^2$; multiplication by $i$ corresponds to a rotation by $90^{\circ }$ counterclockwise.