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2. Complex number - Wikipedia

   en.wikipedia.org/wiki/Complex_number

   Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation =; every complex number can be expressed in the form ...

3. Imaginary number - Wikipedia

   en.wikipedia.org/wiki/Imaginary_number

   An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i 2 = −1. [1] [2] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]

4. Complex geometry - Wikipedia

   en.wikipedia.org/wiki/Complex_geometry

   In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves.

5. Mathematics - Wikipedia

   en.wikipedia.org/wiki/Mathematics

   Analysis is further subdivided into real analysis, where variables represent real numbers, and complex analysis, where variables represent complex numbers. Analysis includes many subareas shared by other areas of mathematics which include: [14] Multivariable calculus; Functional analysis, where variables represent varying functions

6. Root of unity - Wikipedia

   en.wikipedia.org/wiki/Root_of_unity

   In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory , the theory of group characters , and the discrete Fourier transform .

7. Split-complex number - Wikipedia

   en.wikipedia.org/wiki/Split-complex_number

   In algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying =, where . A split-complex number has two real number components x and y , and is written z = x + y j . {\displaystyle z=x+yj.}