Definition:Complex Number as Vector

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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 $P$.