Definition:Complex Number as Vector
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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 $P$.
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Vector Interpretation of Complex Numbers