Results 281 to 290 of about 12,500,740 (339)
Some of the next articles are maybe not open access.
Bird's Engineering Mathematics, 1988
Publisher Summary This chapter provides an overview on complex number. These are represented pictorially on rectangular or Cartesian axes. The horizontal (x) axis is used to represent the real axis and the vertical (y) axis is used to represent the imaginary axis. Such a diagram is called an Argand diagram.
J. Bird
openaire +5 more sources
Publisher Summary This chapter provides an overview on complex number. These are represented pictorially on rectangular or Cartesian axes. The horizontal (x) axis is used to represent the real axis and the vertical (y) axis is used to represent the imaginary axis. Such a diagram is called an Argand diagram.
J. Bird
openaire +5 more sources
Springer Undergraduate Mathematics Series, 2020
Alexander G. Alenitsyn +2 more
semanticscholar +4 more sources
Alexander G. Alenitsyn +2 more
semanticscholar +4 more sources
Why are complex numbers needed in quantum mechanics? Some answers for the introductory level
American Journal of Physics, 2020Complex numbers are broadly used in physics, normally as a calculation tool that makes things easier due to Euler's formula. In the end, it is only the real component that has physical meaning or the two parts (real and imaginary) are treated separately ...
R. Karam
semanticscholar +1 more source
Complex Modular Numbers: Complex Numbers Need not be Complex
The Mathematics Teacher, 1976Most students are faced with the task of solving the equation x2 + 1 = 0 over the real numbers at some time in their algebra classes. After they substitute values for x unsuccessfully, they usually attempt to solve the equivalent equation x2 = -1. They soon realize that it is impossible to square a real number and obtain a negative number.
Susan J. Grant, Ward R. Stewart
openaire +2 more sources
Practical MATLAB for Engineers - 2 Volume Set, 2018
Sergei Kurgalin, Sergei Borzunov
openaire +2 more sources
Sergei Kurgalin, Sergei Borzunov
openaire +2 more sources
Concurrency: Practice and Experience, 1999
Efficient and elegant complex numbers are one of the preconditions for the use of Java in scientific computing. This paper introduces a preprocessor and its translation rules that map a new basic type complex and its operations to pure Java. For the mapping is insufficient to just replace one complex-variable with two double-variables.
Michael Philippsen, Edwin Günthner
openaire +3 more sources
Efficient and elegant complex numbers are one of the preconditions for the use of Java in scientific computing. This paper introduces a preprocessor and its translation rules that map a new basic type complex and its operations to pure Java. For the mapping is insufficient to just replace one complex-variable with two double-variables.
Michael Philippsen, Edwin Günthner
openaire +3 more sources
, 2017 The motivation for this chapter concerns the solvability of equations of degree larger than one which is only partly possible in the domain of real numbers. For example, no negative real number has a real square root. By postulating that the number -1 obtains a square root, we are led to the field of complex numbers.
Jürg Kramer, Anna-Maria von Pippich
openaire +1 more source
1973
Publisher Summary This chapter provides an overview on complex numbers. Each complex number α = a + bi is completely determined by the ordered pair (a, b) of real numbers where a the real part of α and b the imaginary part of α. For each complex number α = a + bi, the complex conjugate α is defined by α = a − bi = a + (−b)i. The conjugate of a − bi is
Harley Flanders, Justin J. Price
openaire +5 more sources
Publisher Summary This chapter provides an overview on complex numbers. Each complex number α = a + bi is completely determined by the ordered pair (a, b) of real numbers where a the real part of α and b the imaginary part of α. For each complex number α = a + bi, the complex conjugate α is defined by α = a − bi = a + (−b)i. The conjugate of a − bi is
Harley Flanders, Justin J. Price
openaire +5 more sources
Anti-commutative Dual Complex Numbers and 2D Rigid Transformation
arXiv.org, 2016We introduce a new presentation of the two dimensional rigid transformation which is more concise and efficient than the standard matrix presentation. By modifying the ordinary dual number construction for the complex numbers, we define the ring of anti ...
Genki Matsuda, S. Kaji, Hiroyuki Ochiai
semanticscholar +1 more source
2014
For example, the polynomial x 2 + 1 does not have any real roots. A new number, called i, is introduced as a root of that polynomial. The complex numbers are all the numbers of the form a + bi where a and b are real numbers. It is a remarkable fact that every polynomial with real coefficients that is not a constant has a complex root.
Peter Rosenthal +2 more
openaire +2 more sources
For example, the polynomial x 2 + 1 does not have any real roots. A new number, called i, is introduced as a root of that polynomial. The complex numbers are all the numbers of the form a + bi where a and b are real numbers. It is a remarkable fact that every polynomial with real coefficients that is not a constant has a complex root.
Peter Rosenthal +2 more
openaire +2 more sources