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2. Split-complex number - Wikipedia

   en.wikipedia.org/wiki/Split-complex_number

   A split-complex number is an ordered pair of real numbers, written in the form = + where x and y are real numbers and the hyperbolic unit [1] j satisfies = + In the field of complex numbers the imaginary unit i satisfies =

3. cis (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Cis_(mathematics)

   x is the argument of the complex number (angle between line to point and x-axis in polar form). The notation is less commonly used in mathematics than Euler's formula , e ix , which offers an even shorter notation for cos x + i sin x , but cis(x) is widely used as a name for this function in software libraries .

4. Frobenius theorem (real division algebras) - Wikipedia

   en.wikipedia.org/wiki/Frobenius_theorem_(real...

   In mathematics, more specifically in abstract algebra, the Frobenius theorem, proved by Ferdinand Georg Frobenius in 1877, characterizes the finite-dimensional associative division algebras over the real numbers. According to the theorem, every such algebra is isomorphic to one of the following: R (the real numbers) C (the complex numbers) H ...

5. Division algebra - Wikipedia

   en.wikipedia.org/wiki/Division_algebra

   These are of course both associative. For a non-associative example, consider the complex numbers with multiplication defined by taking the complex conjugate of the usual multiplication: = ¯. This is a commutative, non-associative division algebra of dimension 2 over the reals, and has no unit element. There are infinitely many other non ...

6. Complex number - Wikipedia

   en.wikipedia.org/wiki/Complex_number

   A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.

7. Division (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Division_(mathematics)

   For division to always yield one number rather than an integer quotient plus a remainder, the natural numbers must be extended to rational numbers or real numbers. In these enlarged number systems , division is the inverse operation to multiplication, that is a = c / b means a × b = c , as long as b is not zero.