Complex Plane - Other Meanings of "complex Plane"

Other Meanings of "complex Plane"

The preceding sections of this article deal with the complex plane as the geometric analogue of the complex numbers. Although this usage of the term "complex plane" has a long and mathematically rich history, it is by no means the only mathematical concept that can be characterized as "the complex plane". There are at least three additional possibilities.

1. 1+1-dimensional Minkowski space, also known as the split-complex plane, is a "complex plane" in the sense that the algebraic split-complex numbers can be separated into two real components that are easily associated with the point (x, y) in the Cartesian plane.
2. The set of dual numbers over the reals can also be placed into one-to-one correspondence with the points (x, y) of the Cartesian plane, and represent another example of a "complex plane".
3. The vector space C×C, the Cartesian product of the complex numbers with themselves, is also a "complex plane" in the sense that it is a two-dimensional vector space whose coordinates are complex numbers.