Bibliography for the complex numbers

unabridged

 

  1. Quantum reality, complex numbers, and the meteorological butterfly effect
    Palmer, Tim N.
    Bulletin of the American Meteorological Society, v 86, n 4, April, 2005, p 519-530, Compendex.
  2. Geometry of Generalized Complex Numbers  
    Anthony A. Harkin;  Joseph B Harkin;
    Mathematics Magazine, Vol. 77, No. 2, April 2004, pp. 118-129.  
  3. Complex Numbers and Plane Geometry  
    Thierry Dana-Picard  
    Int. J. Math. Educ. Sci. Technol., 2003, vol. 34, no. 2, pp. 257-271.
  4. Fast Fourier Transforms Using the Complex Logarithmic Number System
    Arnold M.; Bailey T.; Cowles J.; Walter C.
    The Journal of VLSI Signal Processing, March 2003, vol. 33, no. 3, pp. 325-335(11), Ingenta.  
  5. Geometrical aspects of a relation ordering the field of complex numbers.
    Kaczmarek, Jerzy
    Zeszyty Nauk. Geom. 22 (2002), 39--52, MathSciNet.  
  6. Iterative decoding of codes over complex numbers
    Haring, J.; Han Vinck, A.J.
    IEEE International Symposium on Information Theory - Proceedings, 2001, p 25, Compendex.
  7. Efficient division in the binary representation of complex numbers
    Blest, D.C.; Jamil, T.
    Conference Proceedings - IEEE SOUTHEASTCON, 2001, p 188-195, Compendex.
  8. Drawing with complex numbers.
    Eastwood, Michael; Penrose, Roger
    Math. Intelligencer 22 (2000), no. 4, 8--13, MathSciNet.  
  9. High-speed complex-number multiplications based on redundant binary representation of partial products
    Shin K-W.; Jeon H-W.
    International Journal of Electronics, 1 June 2000, vol. 87, no. 6, pp. 683-702(20), Ingenta.  
  10. Enhanced artificial neural networks using complex numbers
    Michel, Howard E.; Awwal, A.A.S.
    Proceedings of the International Joint Conference on Neural Networks, v 1, 1999, p 456-461, Compendex.
  11. Sums of Complex Numbers of Unit Magnitude   
    Hubert Kiechle; A. N. 't Woord
    The American Mathematical Monthly, Vol. 105, No. 5 (May, 1998), p. 469, Jstor.   
  12. Planar Motion, Complex Numbers, and Falling Leaves: An Intriguing Minilab
    Etkina, E.; Holton, B.; Horton, G.
    Physics Teacher, v 36, n 3, 1998, p 135, Compendex.
  13. Arg (in Notes)  
    John A. Baker; Willem Sluis  
    Mathematics Magazine, Vol. 70, No. 4. (Oct., 1997), p. 291, Jstor.  
  14. Constructing the complex numbers
    Cuoco, A.
    International Journal of Computers for Mathematical Learning, v 2, n 2, 1997, p 155-186, Compendex.
  15. Use of quasi-complex numbers in the calculation of robotic movements-underlying principles in its speediness of computation
    Zhao, Guowen; Pan, Yuxue; Liu, Li; Duan, Xiumin; Chang, Jianping; Hou, Jili; Lu, Guiying
    Binggong Xuebao/Acta Armamentarii, v 18, n 4, Nov, 1997, p 347-349 Language: Chinese, Compendex
  16. Rotations, complex numbers and quaternions
    Tzanakis, C.
    International Journal of Modern Physics A, v 10, n 8, 1995, p 45, Compendex.
  17. Convexity result for complex numbers with applications to nonnegative normal matrices
    Kirkland, Steve; Hartwig, Robert F.
    Linear Algebra and Its Applications, v 221, May, 1995, p 195, Compendex.  
  18. On Santilli's isotopies of the theory of real numbers, complex numbers, quaternions and octonions.
    Kamiya, Noriaki
    New frontiers in algebras, groups and geometries (Monteroduni, 1995), 523--551, Ser. New Front. Adv. Math. Ist. Ric. Base, Hadronic Press, Palm Harbor, FL, 1996, MathSciNet.  
  19. Simplified optical complex multiplication using quater-imaginary number representation
    Guoqiang L.; Liren L.; Changhe Z.
    Optics Communications, 15 December 1995, vol. 122, no. 1, pp. 16-22(7), Ingenta.   
  20. Les nombres complexes hyperboliques: des complexes qui nous laissent perplexes. (French) [Hyperbolic complex numbers: complexes that leave us perplexed]
    Lambert, Dominique
    Rev. Questions Sci. 166 (1995), no. 4, 383--400, MathSciNet.  
  21. Reduced algebraic numbers in the complex plane.
    Wolfskill, John
    J. Number Theory 48 (1994), no. 3, 392--412, MathSciNet.  
  22. Integrated multiplier for complex numbers
    Oklobdzija, Vojin G.; Villeger, David; Soulas, Thierry
    Journal of VLSI Signal Processing Systems for Signal, Image, and Video Technology, v 7, n 3, May, 1994, p 213-222, Compendex.  
  23. Complex numbers and geometry.
    Hahn, Liang-shin
    MAA Spectrum. Mathematical Association of America, Washington, DC, 1994. x+192 pp. ISBN: 0-88385-510-0, MathSciNet.  
  24. A Perspective Into Ligand-Receptor Affinities Using Complex Numbers  
    Irving M. Klotz
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 90, No. 15 (Aug., 1993), pp. 7191-7194, Jstor.  
  25. A note on sums of powers of complex numbers.
    Fabrykowski, J.
    Acta Math. Hungar. 62 (1993), no. 3-4, 209--210, MathSciNet.  
  26. Commutative extended complex numbers and connected trigonometry
    Fleury, N.; De Traubenberg, M. Rausch; Yamaleev, R.M.
    Journal of Mathematical Analysis and Applications, v 180, n 2, Dec, 1993, p 431, Compendex.
  27. On some problems of P. Turán concerning power sums of complex numbers.
    Erdös, L.
    Acta Math. Hungar. 59 (1992), no. 1-2, 11--24, MathSciNet.  
  28. Extending the Complex Number System  
    Pineda, Anton and David C. Arney  
    Math. and Comp. Ed., (1991), V. 25, No. 1, pp. 10-16.  
  29. A Visit to the Newtonian N-Body Problem via Elementary Complex Variables  
    Donald G. Saari  
    American Mathematical Monthly, Vol. 97, No. 2. (Feb., 1990), pp. 105-119, Jstor.  
  30. Eine affingeometrische Anwendung der komplexen Zahlen. (German) [An affine-geometric application of complex numbers]
    Pickert, Günter
    Math. Semesterber. 37 (1990), no. 2, 240--250, MathSciNet.  
  31. Generalizations of a Complex Number Identity (in Classroom Capsules)  
    M. S. Klamkin; Alberta Murty; V. N. Murty  
    The College Mathematics Journal, Vol. 20, No. 5. (Nov., 1989), pp. 415-416, Jstor.  
  32. Parameter Determination for Complex Number-Theoretic Transforms Using Cyclotomic Polynomials  
    R. Creutzburg; M. Tasche
    Mathematics of Computation, Vol. 52, No. 185 (Jan., 1989), pp. 189-200, Jstor.  
  33. Complex number multipliers.
    Pekmestzi, K. Z. Source:
    IEE Proceedings. Part E, Computers and Digital Techniques v. 136 (Jan. '89) p. 70-5, First Search.
  34. Generalized number systems in the complex plane.
    Daróczy, Z.; Kátai, I.
    Acta Math. Hungar. 51 (1988), no. 3-4, 409--416, MathSciNet.  
  35. Die komplexen Zahlen. (German) [The complex numbers] Theorie---Praxis---Geschichte. [Theory---practice---history] Second edition.
    Pieper, Herbert
    Mathematische Schülerbücherei [Mathematical Library for Students], 110. VEB Deutscher Verlag der Wissenschaften, Berlin, 1988. 256 pp. ISBN: 3-326-00406-0, MathSciNet.  
  36. Complex Numbers and Pythagorean Triples  
    Jackson, Margaret  
    The Math. Gazette, (1987), V. 71, No. 456, p. 127  
  37. Power of Complex Numbers  
    Kimberling, Clark  
    The Math. Teach., (1987), V. 80, No. 1, pp. 63-67.  
  38. Complex numbers in mathematics, mechanics and physics. (Italian)
    Duma, Andrei
    Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 65 (1987), 5--16 (1988), MathSciNet.  
  39. Formalism, Hamilton and complex numbers.
    O'Neill, John
    Stud. Hist. Philos. Sci. 17 (1986), no. 3, 351--372, MathSciNet.  
  40. Solvability of Infinite Systems of Polynomial Equations Over the Field of Complex Numbers  
    Alexander Abian  
    American Mathematical Monthly, Vol. 92, No. 2. (Feb., 1985), pp. 94-98, Jstor.  
  41. Archimedes and the Complex Plane  
    George M. Phillips  
    American Mathematical Monthly, Vol. 91, No. 2. (Feb., 1984), pp. 108-114, Jstor.  
  42. Products of Sets of Complex Numbers  
    Byron L. McAllister  
    The Two-Year College Mathematics Journal, Vol. 14, No. 5. (Nov., 1983), pp. 390-397, Jstor.  
  43. Some notes on the power sums of complex numbers whose sum is 0.
    Surányi, J.
    Studies in pure mathematics, 711--717, Birkhäuser, Basel, 1983, MathSciNet.  
  44. Proving Pedoe's Inequality by Complex Number Computation (in Notes)  
    Gengzhe Chang  
    American Mathematical Monthly, Vol. 89, No. 9. (Nov., 1982), p. 692, Jstor.  
  45. Complex numbers with three radix expansions.
    Gilbert, William J.
    Canad. J. Math. 34 (1982), no. 6, 1335--1348, MathSciNet.  
  46. An Identity for Complex Numbers: Problem 80-15 (in Solutions)  
    M. S. Klamkin; A. Meir
    SIAM Review, Vol. 23, No. 3. (Jul., 1981), pp. 395-396, Jstor.  
  47. Applying Complex Arithmetic  
    Herbert L. Holden  
    The Two-Year College Mathematics Journal, Vol. 12, No. 3. (Jun., 1981), pp. 190-194, Jstor.  
  48. A note on ordering the complex numbers.
    Weimer, Richard C.
    A collection of manuscripts related to the Fibonacci sequence, pp. 20--21, Fibonacci Assoc., Santa Clara, Calif., 1980, MathSciNet.  
  49. Algoritmy vypolneniya arifmeticheskikh operatsii nad kompleksnymi chislami v dekartovoi sisteme koordinat. (Russian) [Algorithms for carrying out arithmetic operations over complex numbers in the Cartesian coordinate system] [Preprint 80], 22.
    Semotjuk, M. V.
    Akad. Nauk Ukrain. SSR, Inst. Kibernet., Kiev, 1980. 54 pp., MathSciNet.  
  50. On Euler's Formula [Graphics:../Images/ComplexNumbersBib_gr_2.gif]  
    Subramaniam, K. B.  
    Int. J. of Math. Ed. in Sci. and Tech., (1979), V. 10, No. 2, pp. 279.  
  51. Algebraic Equations Whose Roots Form Regular n-Gons in the Complex Plane (in Classroom Notes)  
    Bolesh J. Skutnik  
    American Mathematical Monthly, Vol. 86, No. 9. (Nov., 1979), pp. 770-771, Jstor.  
  52. Møller Caspar Wessel and the representation of complex numbers. (Danish)
    Pedersen, Kirsti
    Normat No. 2 (1979), 49--55, 87, MathSciNet.  
  53. A criterion for the algebraic dependence of two complex numbers.
    Dvornicich, Roberto
    Boll. Un. Mat. Ital. A (5) 15 (1978), no. 3, 678--687, MathSciNet.  
  54. Can the Complex Numbers Be Ordered? (in Mathematical)  
    Richard C. Weimer  
    The Two-Year College Mathematics Journal, Vol. 7, No. 4. (Dec., 1976), pp. 10-12, Jstor.  
  55. Sets of Complex Numbers  
    D. E. Daykin; A. Wilansky  
    Mathematics Magazine, Vol. 47, No. 4. (Sep., 1974), pp. 228-229, Jstor.  
  56. Shorter Notes: Continued Fractions and Equivalent Complex Numbers  
    Richard B. Lakein  
    Proceedings of the American Mathematical Society, Vol. 42, No. 2. (Feb., 1974), pp. 641-642, Jstor.  
  57. "Complex" and "simple" numbers. (Russian)
    Kanovic, M. I.
    Dokl. Akad. Nauk SSSR 218 (1974), 276--277, MathSciNet.  
  58. Complex Numbers as Residue Classes of Polynomials mod (x^2 + 1) (in Classroom Notes)  
    Rosemary Schmalz  
    The Two-Year College Mathematics Journal, Vol. 3, No. 2. (Autumn, 1972), pp. 78-80, Jstor.  
  59. A Categorical System of Axioms for the Complex Numbers  
    W. Bosch; P. Krajkiewicz  
    Mathematics Magazine, Vol. 43, No. 2. (Mar., 1970), pp. 67-70, Jstor.  
  60. An Inequality About Complex Numbers (in Classroom Notes)  
    W. W. Bledsoe  
    American Mathematical Monthly, Vol. 77, No. 2. (Feb., 1970), pp. 180-182, Jstor.  
  61. An Approach to Complex Numbers  
    Willson, William Wynne  
    The Math. Gazette, (1970), V. 54, No. 390, pp. 342-346.  
  62. Complex Variables and Line-Coordinates  
    R. Kittappa  
    Mathematics Magazine, Vol. 41, No. 5. (Nov., 1968), pp. 269-272, Jstor.  
  63. Automorphisms of the Complex Numbers  
    Paul B. Yale  
    Mathematics Magazine, Vol. 39, No. 3. (May, 1966), pp. 135-141, Jstor.  
  64. Extremal problems for sums of powers of complex numbers.
    Buckholtz, J. D.
    Acta Math. Acad. Sci. Hungar 17 1966 147--153, MathSciNet.  
  65. A Note on the Operation of Multiplication in the Complex Plane (in Classroom Notes)  
    D. J. Hansen  
    American Mathematical Monthly, Vol. 71, No. 2. (Feb., 1964), pp. 185-186, Jstor.  
  66. The generalisation of complex number into space. I. Algebra of space-numbers. (Polish)
    Karwowski, Otomar
    Zeszyty Nauk. Politech. Warszawsk. Mat. No. 83 1964 zeszyt 1, 111--119, MathSciNet.  
  67. Axioms for Complex Numbers (in Mathematical Notes)  
    D. H. Potts  
    American Mathematical Monthly, Vol. 70, No. 9. (Nov., 1963), pp. 974-975, Jstor.  
  68. Plane Geometry and Complex Numbers (in Miscellaneous Notes)  
    Robert G. Blake  
    Mathematics Magazine, Vol. 35, No. 4. (Sep., 1962), pp. 239-242, Jstor.  
  69. A Note on a Theorem in Complex Variables and Applications (in Teaching of Mathematics)  
    Eugene M. Romer  
    Mathematics Magazine, Vol. 35, No. 3. (May, 1962), pp. 173-174, Jstor.  
  70. An extremal problem for sums of powers of complex numbers and an application thereof. (Hungarian)
    Turán, Pál
    Mat. Lapok 13 1962 279--288, MathSciNet.  
  71. Geometry of complex numbers.
    Schwerdtfeger, Hans
    Mathematical Expositions, No. 13 University of Toronto Press, Toronto 1962 xi+186 pp., MathSciNet.  
  72. A combinatorial lemma for complex numbers.
    Baxter, Glen
    Ann. Math. Statist. 32 1961 901--904, MathSciNet.  
  73. Equiangular Complex Numbers (in Classroom Notes)  
    J. P. Ballantine  
    American Mathematical Monthly, Vol. 67, No. 7. (Aug. - Sep., 1960), pp. 674-678, Jstor.  
  74. The Imaginary Number Problem (in Classroom Notes)  
    A. W. McGaughey  
    American Mathematical Monthly, Vol. 64, No. 3. (Mar., 1957), pp. 193-194, Jstor.  
  75. Complex Numbers and Trigonometry  
    D. E. Richmond  
    American Mathematical Monthly, Vol. 64, No. 7. (Aug. - Sep., 1957), pp. 478-485, Jstor.  
  76. Introduction to Complex Numbers  
    Louis E. Diamond  
    Mathematics Magazine, Vol. 30, No. 5. (May - Jun., 1957), pp. 233-249, Jstor.  
  77. Introduction to the geometry of complex numbers.
    Deaux, Roland
    Translated from the revised French edition by Howard Eves. Frederick Ungar Publishing Co., New York, 1957. 208 pp., MathSciNet.  
  78. Complex Numbers and their Graphical Representation  
    Walter B. Carver  
    American Mathematical Monthly, Vol. 63, No. 9, Part 2: The Conjugate Coordinate System for Plane Euclidean Geometry. (Nov., 1956), pp. 1-7, Jstor.  
  79. On sums of series of complex numbers.
    Hanani, Haim
    Pacific J. Math. 3, (1953). 695--709, MathSciNet.  
  80. Introduction of Complex Numbers as Vectors of the Plane (in Classroom Notes)  
    L. Fuchs and T. Szele
    American Mathematical Monthly, Vol. 59, No. 9. (Nov., 1952), pp. 628-631, Jstor.  
  81. Non-Euclidean geometries over the complex and the hypercomplex numbers and their application to real geometries.
    Rozenfel\cprime d, B. A.
    One hundred and twenty-five years of the non-Euclidean geometry of Lobacevskii, 1826--1951, pp. 151--166. Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1952, MathSciNet.  
  82. Complex Numbers and Vector Algebra (in Classroom Notes)  
    D. E. Richmond  
    American Mathematical Monthly, Vol. 58, No. 9. (Nov., 1951), pp. 622-628, Jstor.  
  83. Convergence- and Sum-Factors for Series of Complex Numbers  
    E. Calabi; A. Dvoretzky  
    Transactions of the American Mathematical Society, Vol. 70, No. 1. (Jan., 1951), pp. 177-194, Jstor.  
  84. Sets of complex numbers associated with a matrix.
    Parker, W. W.
    Duke Math. J. 15, (1948). 711--715, MathSciNet.  
  85. A process leading to a ring of complex numbers called "continuized matrices." (Hebrew)
    Hebroni, Pessach
    Riveon Lematematika 1, (1947). 86--90, MathSciNet.  
  86. Use of complex numbers in solving problems of heat transfer by plane thermal waves. C. R. (Doklady)
    Shklover, A. M.
    Acad. Sci. URSS (N.S.) 45, (1944). 106--110, MathSciNet.  
  87. Open Additive Semi-Groups of Complex Numbers  
    Einar Hille; Max Zorn  
    The Annals of Mathematics, 2nd Ser., Vol. 44, No. 3. (Jul., 1943), pp. 554-561, Jstor.  
  88. A Paradox in Complex Numbers and Integration (in Questions, Discussions, and Notes)  
    C. O. Oakley  
    American Mathematical Monthly, Vol. 47, No. 1. (Jan., 1940), pp. 37-39, Jstor.  
  89. Applications of Complex Numbers to Geometry of Circles  
    Allen A. Shaw  
    National Mathematics Magazine, Vol. 14, No. 1. (Oct., 1939), pp. 26-36, Jstor.  
  90. A Note on Geometrical Applications of Complex Numbers (in Questions and Discussions)  
    S. A. Schelkunoff  
    American Mathematical Monthly, Vol. 37, No. 6. (Jun. - Jul., 1930), pp. 301-303, Jstor.  
  91. On the Use of Complex Numbers  
    W. Paul Webber  
    Mathematics News Letter, Vol. 4, No. 4. (Dec., 1929), pp. 15-16, Jstor.  
  92. Some Geometrical Applications of Complex Numbers  
    Lloyd L. Small  
    American Mathematical Monthly, Vol. 36, No. 10. (Dec., 1929), pp. 504-511, Jstor.  
  93. A Contribution of Leibniz to the History of Complex Numbers  
    R. B. McClenon  
    American Mathematical Monthly, Vol. 30, No. 7. (Nov., 1923), pp. 369-374, Jstor.  
  94. Discussions: Definitions of Imaginary and Complex Numbers (in Questions and Discussions)  
    Edward S. Allen  
    American Mathematical Monthly, Vol. 29, No. 8. (Sep., 1922), pp. 301-303, Jstor.  
  95. Discussion: Complex Numbers in Advanced Algebra (in Questions and Discussions)  
    H. E. Webb  
    American Mathematical Monthly, Vol. 27, No. 11. (Nov., 1920), pp. 411-413, Jstor.  
  96. Discussions: Relating to the Graph of Y = f(X) for Complex Variables (in Questions and Discussions)  
    E. L. Rees  
    American Mathematical Monthly, Vol. 25, No. 3. (Mar., 1918), p. 128, Jstor.  
  97. Rational Approximations to Irrational Complex Number  
    Lester R. Ford  
    Transactions of the American Mathematical Society, Vol. 19, No. 1. (Jan., 1918), pp. 1-42, Jstor.  
  98. The Graph of F(X) for Complex Numbers  
    A. F. Frumveller  
    American Mathematical Monthly, Vol. 24, No. 9. (Nov., 1917), pp. 409-420, Jstor.  

 

 

 

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(c) John H. Mathews 2006