Examples of using Complex plane in English and their translations into Turkish
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She's moved on to complex plane multibrots.
Entire function: A holomorphic function whose domain is the entire complex plane.
In control theory, one use of the complex plane is known as the 's-plane.
If you gave some angle and some distance,that would also specify this point in a complex plane.
Hence f(z) takes on the value of every number in the complex plane except for zero infinitely often.
Considered as a Riemann surface,the open unit disk is therefore different from the complex plane.
The concept of the complex plane allows a geometric interpretation of complex numbers.
Under this stereographic projection the northpole itself is not associated with any point in the complex plane.
The complex plane is sometimes called the Argand plane because it is used in Argand diagrams.
When discussing functions of a complex variable itis often convenient to think of a cut in the complex plane.
Take for example the complex plane under the exponential map: the image is C-{0}, which is not simply connected.
Argand diagrams are frequently used to plot the positions of the zeros andpoles of a function in the complex plane.
Take for example the complex plane under the exponential map: the image is C-{0}, which clearly is not simply connected.
As a consequence of Liouville's theorem,any function that is entire on the whole Riemann sphere(complex plane and the point at infinity) is constant.
This topological space, the complex plane plus the point at infinity, is known as the extended complex plane.
Contour integration In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.
So one continuous motion in the complex plane has transformed the positive square root e0 1 into the negative square root eiπ -1.
This allows the extension of the definition of functions, such as the Riemann zeta function, which are initially defined in terms of infinite sums that convergeonly on limited domains to almost the entire complex plane.
The preceding sections of this article deal with the complex plane in terms of a geometric representation of the complex numbers.
Although this usage of the term"complex plane" has a long and mathematically rich history, it is by no means the only mathematical concept that can be characterized as"the complex plane.
Let(X,||||) be a complex Banach space and let B be the open unit ball in X. LetΔ denote the open unit disc in the complex plane C, thought of as the Poincaré disc model for 2-dimensional real/1-dimensional complex hyperbolic geometry.
So for every point on the complex plane, you put that point in for c, and then you start with zero, and you keep doing this.
Rising factorial===Another series developmentusing the rising factorial valid for the entire complex plane is: formula_97This can be used recursively to extend the Dirichlet series definition to all complex numbers.
If U{\displaystyle U} is an open subset of the complex plane C{\displaystyle\mathbb{C}}, then a function f: U→ C{\displaystyle f: U\to\mathbb{C}} is conformal if and only if it is holomorphic and its derivative is everywhere non-zero on U{\displaystyle U.
The Riemann mappingtheorem about the conformal relationship of certain domains in the complex plane, which may be the most important result in the one-dimensional theory, fails dramatically in higher dimensions.
A bigger barrier is needed in the complex plane, to prevent any closed contour from completely encircling the branch point z 0.
The notion of simple connectedness is important in complex analysis because of the following facts: The Cauchy's integral theorem states that if Uis a simply connected open subset of the complex plane C, and f: U→ C is a holomorphic function, then f has an antiderivative F on U, and the value of every line integral in U with integrand f depends only on the end points u and v of the path, and can be computed as F(v)- Fu.
In particular, on any connected open subset of the complex plane, there can be no bump function defined on that set which is holomorphic on the set.
Two-dimensional complex vector space, a"complex plane" in the sense that it is a two-dimensional vector space whose coordinates are complex numbers.
In complex analysis,the open mapping theorem states that if U is a domain of the complex plane C and f: U→ C is a non-constant holomorphic function, then f is an open map i.e. it sends open subsets of U to open subsets of C.