Complex number

In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit i, satisfying i^2 = -1. Every complex number can be written in the form x+iy, where x and y are real numbers called the real part and the imaginary part of the complex number, respectively. Pairs of complex numbers can be added, subtracted, multiplied, and divided in a manner similar to that of real numbers. Formally, one says that the set of all complex numbers forms a field.

Related Topics:
Mathematics - Real number - Imaginary unit - Real part - Imaginary part - Field

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The set of all complex numbers is usually denoted by C, or in blackboard bold by mathbb{C}. It includes the real numbers, so every real number is complex. However, sometimes "complex" is used in the meaning "non-real".

Related Topics:
Set - Blackboard bold

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The system of complex numbers, in contrast to that of the real numbers, has the primary advantage that it is algebraically closed, that is, all non-constant polynomials with complex coefficients have roots in the complex numbers. This result is known as the fundamental theorem of algebra.

Related Topics:
Algebraically closed - Polynomial - Root - Fundamental theorem of algebra

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In mathematics, the term "complex" when used as an adjective means that the field of complex numbers is the underlying number field considered, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra.

Related Topics:
Adjective - Number field - Complex analysis - Complex matrix - Complex polynomial - Complex Lie algebra

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