0820 



General theory of complex numbers 



j. 



Complex numbers. Genocchi, A. Liou 



Mth. 19 (1854) 281-. 



. Pad, P. G. Mt. 11 (1873) 244-. 



. Zolotarev, E. I. [1877] St. Pet. Ac. 



Sc. Bll. 24 (1878) 310-. 



, analysis. Denzler, W. Ziir. Mt. 3 

 (1853-55) 560-. 



, with application to equation ar x + j/ A =2\ 



Kummer, E. E. Berl. Ab. (1857) (Mth.) 



, application to n dimensions. Mollame, V. 



G. Mt. 31 (1893) 271-. 

 comprised in formula a + b *j c. Pepin, 



T. Liouv. J. Mth. 1 (1875) 317-. 



, elementary theory. Hoiiel, J. Bor- 

 deaux Mm. S. Sc. 5 (1867) 1- ; 6 (1868) 1- ; 

 8 (1870) 97-; 1 (1876) 1-. 



formed from roots of unity. Kummer, 

 E. E. Liouv. J. Mth. 12 (1847) 185- ; 

 16 (1851) 377-; Berl. Mb. (1861) 1051- ; 

 (1863) 21-. 



. Kronecker, L. Berl. 



Mb. (1863) 340-. 



. Fuchs, L. [1864] 



Crelle J. 65 (1866) 74-. 



, prime factors. Kummer, 

 E. E. Crelle J. 35 (1847) 327-. 



and 2nd factor of class 

 number. Kummer, E. E. Berl. Mb. (1870) 

 855-. 



, simplest representation. 



Kummer, E. E. Berl. Mb. (1870) 409-. 



w n = l, ideal prime factors. 



Kummer, E. E. Berl. Ab. (1856) (Mth.) 1-. 



Xth roots of unity. Kummer, E. E. 



Crelle J. 40 (1850) 93-, 117-. 



31st roots of unity. Kummer, E. E. 



Berl. Mb. (1870) 755-. 

 , Gaussian representation of. Breuer, A. 



Arch. Mth. Ps. 12 (1894) 337-. 

 geometric representation of a new kind. 



Kotelinikov, A. P. Kazan S. Ps.-Mth. Bll. 



6 (1896) (Prot.) 26. 

 , significance (Schlomilch). Unfer- 



dinger, F. Arch. Mth. Ps. 52 (1871) 252-. 

 , introduction. Baltzer, R. [1882] Crelle 



J. Mth. 94 (1883) 87-. 

 , mechanical interpretation. Zbikovskij, 



A. K. Kazan S. Nt. (Ps.-Mth.) P. 6 (1888) 6. 



, multiplication, geometric significance. 

 Orelli, J. Ziir. Vjschr. 20 (1875) 443-. 



, new method for graphical representation. 



Brill, J. Mess. Mth. 17 (1888) 80-. 

 and their functions, theory. Hertz, K., 



& Dicksttin, S. Par. T. Nauk Sc. Pam. 7 



(*1875) Art. 3, 60 pp. 

 , theorem of Dedekind, proof. Study, E. 



Gott. Nr. (1898) 1-. 

 , theory. Lejeune-Dirichlet, G. Berl. 



Ab. (1841) 141-. 

 , . Kummer, E. E. Berl. B. (1846) 



87-; Crelle J. 35 (1847) 319-. 

 , . Wantzel, L. C. B. 24 (1847) 



430-. 

 , . Bachmann, P. Crelle J. 67 (1867) 



, . Dedekind, E. C. B. 90 (1880) 1205-. 



0820 



Complex numbers, theory. Zolotarev, E. J. 

 Liouv. J. Mth. 6 (1880) 51-, 129-. 



units. Kronecker, L. [1845] Crelle J. 

 Mth. 93 (1882) 1-. 



. Lejeune-Dirichlet, G. Berl. B. (1846) 



103-. 

 . Kronecker, L. Crelle J. 53 (1857) 



176- ; C. B. 96 (1883) 93-, 148-, 216-. 

 . Molk, J. Bll. Sc. Mth. As. 7 (1883) 



(Pt. 1) 133-. 

 , addition to memoir on. Kronecker, L. 



C. B. 99 (1884) 765-. 



, expressions formed from. Kummer, 

 E. E. Crelle J. 50 (1855) 212-. 



Conjugate functions and imaginary logarithms. 

 Hamilton, (Sir) W. R. B. A. Ep. (1834) 

 519-. 



Cube root of >Ja+ bi in form x + yi, simple solu- 

 tion. Simony, O. Arch. Mth. Ps. 55 (1873) 

 72-. 



roots, imaginary, number of (Lockhart). 

 Homer, W. G. Thomson A. Ph. 8 (1816) 

 279-, 388-. 



of unity, theorem of algebra, geometry 



deduced from. Appell, P. C. B. 84 (1877) 



540-. 

 Directive numbers, theorems, and proof of 



Cauchy's theorem on closed contours. Tran- 



son, A. N. A. Mth. 7 (1868) 97-. 

 Discriminants of finite ' ' fields. ' ' Dedekind, R. 



Gott. Ab. 29 (1882) Art. 2, 56 pp. 

 Every equation in one unknown can be 



satisfied by a complex value of this un- 

 known, geometric proof. Wittstein, T. 



Grunert Arch. 6 (1845) 225-. 

 Format's theorem, generalization for Galois 



number fields. Moore, E. H. N. Y. Am. 



Mth. S. Bll. 2 (1896) 189-. 

 G. C. M. of 2 complex numbers, number of 



divisions. Dupre, A. Liouv. J. Mth. 13 



(1848) 333-. 



Geometrical representation of \/-l, considera- 

 tion of objections. Warren, J". Phil. Trans. 



(1829) 241-. 

 Goniometry, application of principles given by 



Warren. Terrot, C. H. [1847] Edinb. B. 



S. T. 16 (1849) 345-. 

 Imaginaries. Buee, . [1805] Phil. Trans. 



(1806) 23-. 

 . Fran^ais, J. F. Gergonne A. Mth. 4 



(1813-14) 222-, 364-. 



. Volpicelli, P. G. Arcad. 52 (1831) 221-. 

 . Bellavitis, G. Poligrafo 5 (1831) 15-; 12 



(1832) 211-. 



. Arenstein, J. Haidinger B. 3 (1847) 292-. 

 . Bellavitis, G. Yen. At. 6 (1847) 459-; 



Yen. Mm. I. 4 (1852) 243-. 

 . Arenstein, J. Haidinger Ab. 2 (1848) 



(Ab. 2) 43-. 



. Cockle, Jas. Ph. Mg. 36 (1850) 281-. 

 . Grunert, J. A. Grunert Arch. 20 (1853) 



121-. 



. Sabatie, J. N. A. Mth. 2 (1863) 206-. 

 . Cheyrezy, U. N. A. Mth. 3 (1864) 445-. 

 . Sexe, S. A. N. Mg. Ntvd. 16 (1869) 1-; 



17 (1870) 233-; Arch. Mth. Ntvd. 7 (1882) 



115-. 



54 



