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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

  • 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.

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