Any numbers being Complex numbers

In summary, the concept of "number" is not well-defined in mathematics and includes a variety of different types, such as real numbers, transfinite numbers, and hyperreal numbers. Complex numbers are a subset of numbers in which the numbers are expressed as a + bi, where a and b are real numbers. However, there are other types of numbers, such as hypercomplex numbers, that are not considered to be subsets of complex numbers. Additionally, numerical quantities described with vectors or tensors cannot be described as complex numbers.
  • #1
Anachronistic
8
1
Are there any numbers that is not considered to be a subset of a complex number subset of

a + bi

Where a and b are real numbers?
 
Physics news on Phys.org
  • #2
Define "number".

I'm asking because the concept of number is not well-defined in mathematics. There are a lot of things which carry the name "number", like real number, transfinite number, p-adic number, hyperreal number, etc. All these things are called numbers and often have no obvious relationship to each other. The concept of a number is too broad. It is not defined in mathematics.
 
Last edited:
  • #3
I don't know as much as micromass on this subject, but I just read this on wikipedia and I think it might interest the OP.

On the wiki page of Number, it says under the header "Complex Numbers" the following:
Sets of numbers that are not subsets of the complex numbers are sometimes called hypercomplex numbers.
which is the same wording at the OP used, so maybe he chould check out hypercomplex numbers.
 
  • #4
Numerical quantities described with vectors of more than two elements or tensors cannot, as a general rule, be described as complex numbers.
 
  • #5


Yes, there are numbers that are not considered to be a subset of the complex numbers. These numbers are known as transcendental numbers, such as pi and e. These numbers cannot be expressed as a combination of real numbers a and b, thus they are not considered to be a subset of the complex numbers. Additionally, there are other types of numbers, such as imaginary numbers and quaternions, that are not subsets of the complex numbers. Therefore, while the complex numbers are a subset of the real numbers, not all numbers can be represented as a + bi.
 

What are complex numbers?

Complex numbers are numbers that contain both a real part and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part with i being the square root of -1.

What is the purpose of complex numbers?

Complex numbers are used to represent quantities that cannot be expressed using only real numbers. They are often used in mathematics, physics, and engineering to solve problems involving wave functions, electrical circuits, and quantum mechanics.

How do you add or subtract complex numbers?

To add or subtract complex numbers, simply combine the real parts and the imaginary parts separately. For example, (2+3i) + (4+2i) = (2+4) + (3+2)i = 6+5i. Similarly, to subtract, you would subtract the real parts and the imaginary parts separately.

Can complex numbers be multiplied or divided?

Yes, complex numbers can be multiplied and divided. To multiply complex numbers, use the FOIL method (First, Outer, Inner, Last) and remember that i squared is equal to -1. To divide complex numbers, use the complex conjugate of the denominator to simplify the expression.

What is the difference between real numbers and complex numbers?

Real numbers are numbers that can be expressed on a number line and include both positive and negative numbers. Complex numbers, on the other hand, include both a real part and an imaginary part and cannot be represented on a number line. Real numbers are a subset of complex numbers, as all real numbers can be expressed as a complex number with an imaginary part of 0.

Similar threads

  • Linear and Abstract Algebra
Replies
1
Views
630
  • Linear and Abstract Algebra
Replies
14
Views
453
  • Linear and Abstract Algebra
Replies
1
Views
694
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
1
Views
842
  • Linear and Abstract Algebra
Replies
11
Views
1K
  • Linear and Abstract Algebra
Replies
6
Views
710
  • Precalculus Mathematics Homework Help
Replies
20
Views
818
Replies
2
Views
697
  • General Math
Replies
7
Views
1K
Back
Top