The field of complex numbers

by Anna Justyna Milewska

Venue:	Journal of Formalized Mathematics
Citations:	24 - 1 self

Datum	Value	Source
TITLE	The field of complex numbers	INFERENCE
AUTHOR NAME	Anna Justyna Milewska	SVM HeaderParse 0.2
AUTHOR AFFIL	University of Białystok; Summary. This article contains the Hahn Banach theorem in the vector space over	SVM HeaderParse 0.2
ABSTRACT	[14], [5], [10], and [9] provide the notation and terminology for this paper. The following propositions are true: 1. PRELIMINARIES (1) For every element z of C holds \|\|z\| \| = \|z\|. (2) For all real numbers x1, y1, x2, y2 holds (x1 + y1i) ·(x2 + y2i) = (x1 · x2 − y1 · y2)+(x1 · y2 + x2 · y1)i. (3) For every real number r holds (r+0i) · i = 0+ri. (4) For every real number r holds \|r+0i \| = \|r\|. (5) For every element z of C such that \|z \| � = 0 holds \|z\|+0i = z \|z\|+0i · z. 2. SOME FACTS ON THE FIELD OF COMPLEX NUMBERS Let x, y be real numbers. The functor x+yiCF yielding an element of CF is defined as follows: (Def. 1) x+yiCF = x+yi. The element iCF of CF is defined as follows: (Def. 2) iCF = i. We now state several propositions: (6) iCF = 0+1i and iCF = 0+1iCF.	SVM HeaderParse 0.2
VENUE	Journal of Formalized Mathematics	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	2001	INFERENCE
VOLUME	12	INFERENCE
CITATIONS	21 found	ParsCit 1.0