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The formula is still valid if x is a complex number, and is also called Euler's formula in this more general case. [1] Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2]
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.}
The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics. Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example).
Cauchy integral theorem (complex analysis) Cauchy-Binet formula (linear algebra) Cauchy–Hadamard theorem (complex analysis) Cauchy–Kowalevski theorem (partial differential equations) Cauchy's theorem ; Cauchy's theorem (finite groups) Cayley–Bacharach theorem (projective geometry) Cayley–Hamilton theorem (Linear algebra)
Using LaTeXiT, one can drag and drop complex math formulas to a number of apps -- Pages, Keynote and TextEdit, to name a few. While the LaTeXiT workflow is fairly simple and straightforward ...
The analogue of Euler's formula for the split-complex numbers is exp ( j θ ) = cosh ( θ ) + j sinh ( θ ) . {\displaystyle \exp(j\theta )=\cosh(\theta )+j\sinh(\theta ).} This formula can be derived from a power series expansion using the fact that cosh has only even powers while that for sinh has odd powers. [ 2 ]
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...
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