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Stirling Numbers for Complex Arguments
SIAM Journal on Discrete Mathematics, 1997The authors define the Stirling numbers for the case of a complex argument by invoking the Cauchy integral formula. Some of the usual identities extend, but others do not. The properties of unimodality and monotonicity do extend.
B. RICHMOND, MERLINI, DONATELLA
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Representation for Complex Numbers
IBM Journal of Research and Development, 1978This communication suggests the feasibility of a single-component scheme for representing complex numbers with real bases. Several advantages are pointed out, including the very simple extraction of the real and imaginary parts of a complex number.
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On the Multiplication of Complex Numbers
The Mathematical Gazette, 1949In the development of the theory of complex numbers, it is important to give a definition of them dependent only upon real numbers. In the usual algebraic treatments the product is postulated in the form or obtained from a matrix representation.
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2016
We introduced complex numbers in Sect. 1.8 of the first volume. There we just defined the numbers themselves, but did not go any further. In fact, since the introduction of complex numbers a number of centuries ago, the theory based on them has been substantially developed into an extended analysis of complex functions defined on the complex plane. The
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We introduced complex numbers in Sect. 1.8 of the first volume. There we just defined the numbers themselves, but did not go any further. In fact, since the introduction of complex numbers a number of centuries ago, the theory based on them has been substantially developed into an extended analysis of complex functions defined on the complex plane. The
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1970
The solution of a quadratic equation ax2 + bx + c = 0 can, of course, be obtained by the formula.
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The solution of a quadratic equation ax2 + bx + c = 0 can, of course, be obtained by the formula.
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1970
In Part 1 of this programme on Complex Numbers, we discovered how to manipulate them in adding, subtracting, multiplying and dividing. We also finished Part 1 by seeing that a complex number a + jb can also be expressed in Polar Form, which is always of the form r(cos θ + j sin θ).
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In Part 1 of this programme on Complex Numbers, we discovered how to manipulate them in adding, subtracting, multiplying and dividing. We also finished Part 1 by seeing that a complex number a + jb can also be expressed in Polar Form, which is always of the form r(cos θ + j sin θ).
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A ``Binary'' System for Complex Numbers
Journal of the ACM, 1965Computer operations with complex numbers are usually performed by dealing with the real and imaginary parts separately and combining the two as a final operation. It might be an advantage in some problems to treat a complex number as a unit and to carry out all operations in this form.
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