# Definition:Complex Number as Vector

## Definition

Let $z = x + i y$ be a complex number.

Then $z$ can be considered as a vector $OP$ in the complex plane such that:

its initial point is the origin
its terminal point $P$ is the point $\tuple {x, y}$.

Two vectors which have the same magnitude and direction, but different initial points, are considered equal.

## Also known as

The vector $OP$ is also known as the position vector of $P$.