Abstract
The introduction of complex numbers into algebra is connected with the solution of quadratic equations. The sum, difference, product, and quotient of the numbers conjugate to two given complex numbers are respectively conjugate to the sum, difference, product, and quotient of those numbers. Complex numbers can be added, subtracted, multiplied, and divided, and all the laws that these operations satisfy agree with the laws of operation for ordinary real numbers. There exists a unique complex number 0 = 0 + 0i, for which division is impossible. Even though in the field of real numbers the extraction of a square root is possible only in the case of a positive number—more precisely, of a non-negative number, in the field of complex numbers the square root of any number z = a + bi can be extracted. It is shown that every quadratic equation—with real or generalized complex coefficients—has two (coincident or distinct) roots in the field of generalized complex numbers.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Complex Numbers in Geometry
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
