Complex Plane Dimension Number

In summary: There are even more differences than that, so they really aren't related other than that they both use the word "dimension".In summary, the concept of a complex plane, used in complex number theory, is a mathematical abstraction that is different from the physical dimensions, including the 11 dimensions in brane theory. While the complex plane is used to visualize complex functions, the 11 dimensions are a part of physical space-time. They are two separate and distinct concepts.
  • #1
Terry Giblin
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What dimension between space-time and 11 Dimensions is allocated to the complex plane 'visualized' and used in complex number theory?

Complex numbers are used in every branch of maths and physics, based on an imaginary complex plane, z = x +iy where y is an imaginary axis and i^2=-1. - It's another Dimension, the imaginary '5th' dimension.

In the current theories, what is name or number of is this dimension apart from the obvious 'imaginary dimension' - what number is it given?

Regards

Terry Giblin
 
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  • #2
You seem to be mixing up several concepts in physics and mathematics
that are different.

To properly visualize a complex function like [tex] f(z) = z^\frac{2}{3} [/tex],
you would like 4 dimensions because the domain of the function is two-dimensions
and so is the range. This can't be done easily, so people usually plot |f(z)| which
is a scalar against z which is two dimensional. The result is a three-dimensional
surface plot.
 
  • #3
What dimension between space-time and 11 Dimensions is allocated to the complex plane 'visualized' and used in complex number theory?
You are mixing up two different (although similar in some ways) concepts. The 11 dimensions of brane theory are physical dimensions, like space and time. The complex plane is a mathematical abstraction. One obvious difference is that for physical dimensions the numbers are in units of length or time, which can be changed (like from feet to meters). The numbers in the complex plane are absolute, e.g. 1 is 1 and nothing else - there is no concept of feet or seconds.
 

What is a complex plane dimension number?

A complex plane dimension number, also known as a complex dimension, is a numerical value that measures the complexity or intricacy of a mathematical object in a complex plane. It is a measure of how many different patterns or structures can exist within a given area of the complex plane.

How is a complex plane dimension number calculated?

The calculation of a complex plane dimension number involves counting the number of patterns or structures within a specific area of the complex plane, and then taking the logarithm of that number. This process is repeated for smaller and smaller areas, and the resulting values are averaged to determine the final dimension number.

What types of objects can have a complex plane dimension number?

A complex plane dimension number can be assigned to various mathematical objects, such as fractals, chaotic systems, and self-similar structures. It can also be used to measure the complexity of real-world systems, such as the human brain or the stock market.

What does a higher complex plane dimension number indicate?

A higher complex plane dimension number indicates a greater level of complexity in the mathematical object being measured. This means that there are more intricate patterns and structures within the given area of the complex plane, and it may require more complex mathematical tools to fully understand and analyze.

How is a complex plane dimension number useful in scientific research?

Complex plane dimension numbers can provide valuable insights into the complexity of various systems, and how they may behave under certain conditions. They can also be used to compare different systems and determine which may be more complex or more simple. Additionally, they can help scientists identify underlying patterns and relationships within complex systems.

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