Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Jorge asked in Science & MathematicsMathematics · 7 years ago

Is the set of complex number a subset of any other type of numbers?

For example, we know that the natural numbers are a subset of the real numbers

And the real numbers are a subset of the complex numbers.

So, are the complex numbers a subset of any other type of numbers?

1 Answer

Relevance
• 7 years ago
Favorite Answer

Yes. Complex numbers can be considered a subset of the quaternions. Quaternions were invented by Hamilton in the 1800s and have the following properties:

There are 3 basis numbers i,j,k for which i^2 = j^2 = k^2 = -1

ij = -ji = k

jk = -kj = i

ki = - ik = j

Notice that for quaternion bases, multiplication is anti-commutative and that it parallels the vector cross-product.

A general quaternion is written as a + bi + cj + dk where a,b,c,d are real numbers.

If we set c=d=0, then we get a + bi which is of course a regular complex number.

Also quaternions themselves are a subset of octonions (invented by Cayley).

This is a big topic I can't even begin to cover on Yahoo Answers. But you can go to wikipedia if you're interested.

Still have questions? Get your answers by asking now.