What is a complex conjugate in mathematics?

In mathematics, a complex conjugate is a pair of two -component numbers called complex numbers. Each of these complex numbers has a real number added to the imaginary folder. Although their value is the same, the sign of one of the imaginary components in a pair of complex conjugate numbers is the opposite of the other sign. Although they have imaginary components, complex conjugates are used to describe physical reality. The use of complex conjugates works despite the presence of imaginary components, because when both components are multiplied together, the result is a real number. This can be repeated by other conditions for simplification. The imaginary number is any real number multiplied by the role of the negative (-1) -Samo incomprehensible. In this form, a complex conjugate is a pair of numbers that can be written, y = a+bi and y = a - Bi, where "i" is a role root -1. Formalistically, to distinguish two Y values, one is generally written with a stick over a letter, ӯ, although an asterisk is sometimes used.

Demonstration that the multiplication of two complex conjugates numbers creates a real result, consider the example, y = 7+2i and ӯ = 7–2i. The multiplication of these two gives yӯ = 49+14i - 14i - 4i ^{2 = 49+4 = 53. Such a real result of comprehensive multiplication of conjugates is important, especially when considering the atomic and sub -atomic levels. Mathematical expressions for small physical systems often include an imaginary component. A discipline in which this is particularly important is quantum mechanics, non -classical physics very small.}

In quantum mechanics, the properties of the physical system consisting of a particle are described by a wave equation. Everything to learn about the particle of its system can be revealed by these equations. Wave equations often have an imaginary component. Multipling the equation of its complex conjugated leads to a physically interpretable “probability density”. Characteristics of particles can be determined by Matemath manipulation with this probability density.

For example, the use of probability density is important in a discrete spectral emission of radiation from atoms. Such a probability density application is called a "born probability" after German physicist Max Born. An important closely related statistical interpretation that the measurement of the quantum system will provide certain specific results is called the Born rule. Max Born was the recipient of the 1954 Nobel Prize in physics for his work in this area. Unfortunately, attempts to derive the born rules from other mathematical derivatives have encountered mixed results.