Results 281 to 290 of about 1,858,099 (308)
Some of the next articles are maybe not open access.
1999
The real number system consists of both the rational numbers (numbers with terminating or repeating decimal expansions) and the irrational numbers (numbers with infinite, non-repeating decimal expansions). The real numbers are denoted by the symbol ℝ. We let ℝ2 = {(x,y : x ∈ ℝ, y ∈ ℝ} (Figure 1.1).
openaire +1 more source
The real number system consists of both the rational numbers (numbers with terminating or repeating decimal expansions) and the irrational numbers (numbers with infinite, non-repeating decimal expansions). The real numbers are denoted by the symbol ℝ. We let ℝ2 = {(x,y : x ∈ ℝ, y ∈ ℝ} (Figure 1.1).
openaire +1 more source
2011
Chapter 4 describes the complex plane which provides a graphical representation for complex numbers. The chapter also contains historical information about the complex plane’s invention, and complements similar historical events associated with quaternions.
openaire +1 more source
Chapter 4 describes the complex plane which provides a graphical representation for complex numbers. The chapter also contains historical information about the complex plane’s invention, and complements similar historical events associated with quaternions.
openaire +1 more source
Fractional derivatives in complex planes
Nonlinear Analysis: Theory, Methods & Applications, 2009Some properties regarding the Caputo derivative defined on real lines are studied. These properties include the expression of the Caputo derivative operator in analytic function space, and homogeneous property. Then some properties such as consistency, compositions of the Ortigueira derivative defined in the complex plane are obtained.
Li, Changpin, Dao, Xuanhung, Guo, Peng
openaire +1 more source
Injectivity Conditions in the Complex Plane
Complex Analysis and Operator Theory, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
2017
In the eighteenth century and earlier, complex numbers were called imaginary numbers and were manipulated algebraically without giving them any geometric meaning. In the early nineteenth century the concept of the complex plane was formulated with the real and imaginary parts of complex numbers corresponding to points in the Euclidean plane.
openaire +1 more source
In the eighteenth century and earlier, complex numbers were called imaginary numbers and were manipulated algebraically without giving them any geometric meaning. In the early nineteenth century the concept of the complex plane was formulated with the real and imaginary parts of complex numbers corresponding to points in the Euclidean plane.
openaire +1 more source
1992
Abstract Complex analysis has its roots in the algebraic, geometric, and topological structure of the complex plane. This chapter starts to explore these foundations. It is assumed that the reader has previously been introduced to complex numbers, and has had some practice in manipulating them.
openaire +1 more source
Abstract Complex analysis has its roots in the algebraic, geometric, and topological structure of the complex plane. This chapter starts to explore these foundations. It is assumed that the reader has previously been introduced to complex numbers, and has had some practice in manipulating them.
openaire +1 more source
2023
Definition, and formulation of the complex plane, as the basis for deriving Euler's identity. From which complex squares, and primes are derived; and the value of pi approximated.
openaire +1 more source
Definition, and formulation of the complex plane, as the basis for deriving Euler's identity. From which complex squares, and primes are derived; and the value of pi approximated.
openaire +1 more source
1991
Complex harmonic plane waves, which are characterized by a complex wave-vector and a complex frequency, may be divided into homogeneous plane waves (having parallel propagation and attenuation vectors) and nonhomogeneous or inhomogeneous plane waves. The last ones may be evanescent plane waves (having perpendicular propagation and attenuation vectors ...
openaire +1 more source
Complex harmonic plane waves, which are characterized by a complex wave-vector and a complex frequency, may be divided into homogeneous plane waves (having parallel propagation and attenuation vectors) and nonhomogeneous or inhomogeneous plane waves. The last ones may be evanescent plane waves (having perpendicular propagation and attenuation vectors ...
openaire +1 more source
The American Mathematical Monthly, 2000
function theory." (In later editions, he did include a proof of part of this theorem, to illustrate the power of the concept of winding number for closed curves. It is worth mentioning that the notion of winding number is never used in this article.) It turns out that the basic facts about topology in R2 can be explained efficiently by identifying the ...
openaire +1 more source
function theory." (In later editions, he did include a proof of part of this theorem, to illustrate the power of the concept of winding number for closed curves. It is worth mentioning that the notion of winding number is never used in this article.) It turns out that the basic facts about topology in R2 can be explained efficiently by identifying the ...
openaire +1 more source
The Complex Plane, Relations, Functions
2020A complex number is an ordered pair of real numbers. If each of (a, b) and (c, d) is a complex number then addition and multiplication are defined on the set of complex numbers in the following way: $$\displaystyle \begin {array}{c} (a,b) + (c,d) = (a+c,b+d)\\ (a,b) (c,d)=(a c-b d, a d+b c) \end {array} $$
openaire +1 more source