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- Q4230058 subject Q6103418.
- Q4230058 subject Q6863978.
- Q4230058 subject Q7216206.
- Q4230058 abstract "In mathematics, a complex-valued function (sometimes referred to as complex function) is a function whose values are complex numbers. In other words, it is a function that assigns a complex number to each member of its domain. This domain does not necessarily have any structure related to complex numbers. Most important uses of such functions in complex analysis and in functional analysis are explicated below.A vector space and a commutative algebra of functions over complex numbers can be defined in the same way as for real-valued functions. Also, any complex-valued function f on an arbitrary set X can be considered as an ordered pair of two real-valued functions: (Ref, Imf) or, alternatively, as a real-valued function φ on X × {0, 1} (the disjoint union of two copies of X) such that for any x:Re f(x) = F(x, 0)Imf(x) = F(x, 1)Some properties of complex-valued functions (such as measurability and continuity) are nothing more than corresponding properties of real-valued functions.".
- Q4230058 thumbnail ExponentielleComplexe_Puissances2.png?width=300.
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- Q4230058 comment "In mathematics, a complex-valued function (sometimes referred to as complex function) is a function whose values are complex numbers. In other words, it is a function that assigns a complex number to each member of its domain. This domain does not necessarily have any structure related to complex numbers.".
- Q4230058 label "Complex-valued function".
- Q4230058 depiction ExponentielleComplexe_Puissances2.png.