Transcription of 1 Complex algebra and the complex plane - MIT Mathematics
{{id}} {{{paragraph}}}
Example: stock market
1 Complex algebra and the complex plane - MIT Mathematics
Topic 1 NotesJeremy Orloff1 Complex algebra and the Complex planeWe will start with a review of the basic algebra and geometry of Complex numbers. Mostlikely you have encountered this previously in or MotivationThe equationx2= 1 has no real solutions, yet we know that this equation arises naturallyand we want to use its roots. So we make up a new symbol for the roots and call it acomplex symbols iwill stand for the solutions to the equationx2= 1. We willcall these new numbers Complex numbers. We will also write 1 = iNote: Engineers typically usejwhile mathematicians and physicists usei. We ll follow themathematical custom in numberiis called animaginary number.
1.2 Fundamental theorem of algebra One of the reasons for using complex numbers is because allowing complex roots means every polynomial has exactly the expected number of roots. This is called the fundamental theorem of algebra. 1Our motivation for using complex numbers is not the same as the historical motivation. Historically,
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: