Examples of using Complex plane in English and their translations into Serbian
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Colloquial
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Ecclesiastic
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Cyrillic
She's moved on to complex plane multibrots.
The gamma function is meromorphic in the whole complex plane.
Manage a highly complex plane above the clouds.
The number 1 has n different nth roots in the complex plane, namely.
On the complex plane, this distance is expressed as i√3 mentioned below.
Thus finding nth roots in the complex plane can be segmented into two steps.
Every complex number has n different nth roots in the complex plane.
The most commonly used are the real line, the complex plane, Euclidean space, other vector spaces, and the integers.
Geometric representation of z andits conjugate z̅ in the complex plane.
But in the complex plane, if a function f(z) is differentiable in a neighborhood it must also be infinitely differentiable in that neighborhood.
These roots are evenly spaced around the unit circle in the complex plane, at angles which are multiples of.
Since we have only one equation but n variables,infinitely many solutions exist(and are easy to find) in the complex plane;
Which introduces a branch cut in the complex plane along the positive real axis with the condition 0≤ θ< 2π, or along the negative real axis with- π< θ≤ π.
There is a unique analytic extension of the zeta function to the rest of the complex plane, except at s= 1.
For any affine transformation of the complex plane, z↦ a z+ b, a≠ 0,{\displaystyle z\mapsto az+b,\quad a\neq 0,} a triangle is transformed but does not change its shape.
Holomorphic functions are complex functions defined on an open subset of the complex plane that are differentiable.
An alternative way of defining a point Z in the complex plane, other than using the x- and y-coordinates, is to use the distance r of the point from O, the point whose coordinates are(0,0)(the origin), together with the angle subtended between the positive real axis and the line segment OZ in a counterclockwise direction.
In fact there are 24 solutions, known as the Kummer solutions, derivable using various identities,valid in different regions of the complex plane.
Since eitz is an entire function(having no singularities at any point in the complex plane), this function has singularities only where the denominator z2+ 1 is zero.
For example, the state space for position and momentum states is the space of square-integrable functions,while the state space for the spin of a single proton is just the product of two complex planes.
Nonetheless, the so-defined function f has a unique analytic continuation to the complex plane with the point x= 1/2 deleted, and it is given by the same rule f(x)= 1/1- 2x.
In mathematics, the Cauchy integral theorem(also known as the Cauchy-Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy(and Édouard Goursat),is an important statement about line integrals for holomorphic functions in the complex plane.
Much of analysis happens in some metric space;the most commonly used are the real line, the complex plane, Euclidean space, other vector spaces, and the integers.
The exact nature of this Hilbert space is dependent on the system- for example, the state space for position and momentum states is the space of square-integrable functions,while the state space for the spin of a single proton is just the product of two complex planes.
As with square roots, the formula above does not define a continuous function over the entire complex plane, but instead has a branch cut at points where θ/ n is discontinuous.
The exact nature of this Hilbert space is dependent on the system â for example, the state space for position and momentum states is the space of square-integrable functions,while the state space for the spin of a single proton is just the product of two complex planes.
Since we have only one equation but n variables,infinitely many solutions exist(and are easy to find) in the complex plane; however, the problem becomes impossible if solutions are constrained to integer values only.
The first term li(x) is the usual logarithmic integral function; the expression li(xρ) in the second term should be considered as Ei(ρ ln x),where Ei is the analytic continuation of the exponential integral function from negative reals to the complex plane with branch cut along the positive reals.
The expression li(xρ) in the second term should be considered as Ei(ρ ln x),where Ei is the analytic continuation of the exponential integral function from negative reals to the complex plane with branch cut along the positive reals.