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2. 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.

3. Fundamental theorem of algebra - Wikipedia

   en.wikipedia.org/wiki/Fundamental_theorem_of_algebra

   Every rational function in one variable x, with real coefficients, can be written as the sum of a polynomial function with rational functions of the form a/(x − b) n (where n is a natural number, and a and b are real numbers), and rational functions of the form (ax + b)/(x 2 + cx + d) n (where n is a natural number, and a, b, c, and d are ...

4. Liouville's theorem (complex analysis) - Wikipedia

   en.wikipedia.org/wiki/Liouville's_theorem...

   Download as PDF; Printable version; ... (Fundamental theorem of algebra) ... If the image of is not dense, then there is a complex number and a real ...

5. 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 ...

6. Hypercomplex number - Wikipedia

   en.wikipedia.org/wiki/Hypercomplex_number

   The complex numbers are the only 2-dimensional hypercomplex algebra that is a field. Split algebras such as the split-complex numbers that include non-real roots of 1 also contain idempotents and zero divisors (+) =, so such algebras cannot be division algebras.

7. Cayley–Dickson construction - Wikipedia

   en.wikipedia.org/wiki/Cayley–Dickson_construction

   As a complex number consists of two independent real numbers, they form a two-dimensional vector space over the real numbers. Besides being of higher dimension, the complex numbers can be said to lack one algebraic property of the real numbers: a real number is its own conjugate.