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Imaginary part of a complex number

AIMAG Returns the imaginary part of a complex number... [Pg.122]

Since the real and imaginary parts of a complex number are independent of each other, a complex number is always specified in terms of two real numbers, like the coordinates of a point in a plane, or the two components of a two-dimensional vector. In an Argand diagram a complex number is represented as a point in the complex plane by a real and an imaginary axis. [Pg.8]

The imaginary part of a complex number x+iy where x and y are real is y. incenter... [Pg.176]

Recognize the real and imaginary parts of a complex number expressed in either cartesian or plane polar coordinates... [Pg.28]

The imaginary part of any complex number is a real number multiplied by i = V. (The symbol = is used throughout this text to indicate a definition, as opposed to the = symbol, used for equalities that can be proved mathematically.) This relationship between i and — 1 allows the imaginary part of a complex number to influence the real-number results of an algebraic operation. For example, if a and b are both real numbers, then a + ib is complex, with a the real part and ib the imaginary part. The complex conjugate of a -F ib, written (fl + ib), is equal to a — ib, and the product of any number with its complex conjugate is a real number ... [Pg.8]

A relationship, known as Euler s formula, exists between a complex number [x + jy] (x is the real part, y is the imaginary part of the complex number (j = P )) and a sine and cosine function. Many authors and textbooks prefer the complex number notation for its compactness and convenience. By substituting the Euler equations cos(r) = d + e -")/2 and sin(r) = (d - e t )l2j in eq. (40.1), a compact complex number notation for the Fourier transform is obtained as follows ... [Pg.516]

Presented in this manner, the analysis may proceed similarly to the treatment obtained from the Fourier analysis. C is the zero frequency component of the fit and A and B may be treated as the real and imaginary parts of the complex number. [Pg.93]

The real and imaginary parts of the complex numbers used here have no physical significance. This is simply a convenient way to represent the component vectors of stress and strain in a dynamic mechanical experiment. [Pg.409]

Multiplication of a complex number by a scalar (real number) is achieved by simply multiplying the real and imaginary parts of the complex number by the scalar quantity. Multiplication of two complex numbers is performed by expanding the expression (a + ih) c + id) as a. sum of terms, and then collecting the real and imaginary parts to yield a new complex number. [Pg.30]

The real part of a complex number is denoted by x = 8fz and the imaginary part by y = Sz. The complex conjugate z (written as z in some books) is the number obtained by changing i to —i ... [Pg.43]

The last two procedures shown in the Complex class declaration are used to extract the real and imaginary parts of a complex munber. For example, the following statement assigns the imaginary part of a, which is a Complex, to X, which is a double number. [Pg.33]

The real numbers a and b are the real and imaginary parts of the complex number (a,b). The terms real and imaginary are historical accidents since both a and b are real numbers, and complex numbers are often useful to describe real phenomena. It is easy to see from ... [Pg.816]

The parameters of the Hamiltonian (3), i.e. the frequencies and the number of oscillators (more specifically, the strength of oscillators) are determined by the imaginary part of a complex dielectric function a(k, co) which characterizes the dielectric losses for polarization fluctuations in a medium. This model is, strictly speaking, applicable to homogeneous isotropic media in which the spatial correlations of polarization fluctuations SP r)dP r ), which determine the dependence of s k, co) on the wave vector k, depend on the difference of coordinates r—r only. [Pg.15]

The number is approximated to the last digit in the fractional part The imaginary unit of a complex number is marked as i but not j The background is white and the numbers are black etc ... [Pg.190]

Let us consider a complex number plane. On the abscissa we shall put the real part of a complex number and on the ordinates its imaginary part (Figure 2.6). Then any complex number can be written as... [Pg.110]

Complex plane plot — The complex number Z = Z + iZ", where i = v/-i, can be represented by a point in the Cartesian plane whose abscissa is the real part of Z and ordinate the imaginary part of Z. In this representation the abscissa is called the real axis (or the axis of reals) and the ordinate the imaginary axis (the axis of imaginaries), the plane OZ Z" itself being referred to as the complex plane [i]. The representing point of a complex number Z is referred to as the point Z. [Pg.106]

If the real and imaginary parts of the complex quantity (number) Z are a function of a certain scalar argument, such as the angular velocity to, as co varies, the complex number Z traces a curve which is called... [Pg.106]

Hence attenuation is considered as an imaginary part of the wave number. (There are also fundamental physical justifications for this, but these need not be addressed here.) This correspondingly forces sound speed to also become a complex quantity ... [Pg.212]

As is evident m the graphical representation of a complex number in Figure 1.1, two complex numbers are equal if and only if both the real and the imaginary parts are equal. Thus, an equation involving complex variables requires that two equations are satisfied, one involving the real terms, and one involving the imaginary terms. Commutative, associative, and distributive laws hold for complex... [Pg.9]


See other pages where Imaginary part of a complex number is mentioned: [Pg.11]    [Pg.31]    [Pg.103]    [Pg.385]    [Pg.486]    [Pg.15]    [Pg.249]    [Pg.486]    [Pg.8]    [Pg.18]    [Pg.697]    [Pg.124]    [Pg.230]    [Pg.512]    [Pg.11]    [Pg.31]    [Pg.103]    [Pg.385]    [Pg.486]    [Pg.15]    [Pg.249]    [Pg.486]    [Pg.8]    [Pg.18]    [Pg.697]    [Pg.124]    [Pg.230]    [Pg.512]    [Pg.102]    [Pg.208]    [Pg.126]    [Pg.136]    [Pg.189]    [Pg.2267]    [Pg.17]    [Pg.193]    [Pg.60]    [Pg.30]    [Pg.303]    [Pg.26]    [Pg.84]   
See also in sourсe #XX -- [ Pg.3 , Pg.45 ]

See also in sourсe #XX -- [ Pg.3 , Pg.45 ]

See also in sourсe #XX -- [ Pg.29 ]




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