Transcription of Complex Numbers - Bilkent University
{{id}} {{{paragraph}}}
Example: air traffic controller
Complex Numbers - Bilkent University
Numbers are Numbers of the forma+bi, whereaandbare real, andwhereiis an element withi2= 1. Complex Numbers , just as the real Numbers ,form a field: (a+bi) + (c+di) = (a+c) + (b+d)i, (a+bi)(c+di) = (ac bd) + (ad+bc)i; a+bic+di=(a+bi)(c di)(c+di)(c di)=ac+bdc2+d2+bc adc2+d2iwheneverc+di6= elementa+bi=a biis called the conjugate ofa+bi, the map itself is calledcomplex :(1)xy=xy;(2)x=x;(3)x=xif and only ifxis real;(4)x= xif and only ifxis imaginary, , ifx=bifor some just as there are real vector spaces (sets of elements that can be added andmultiplied by real Numbers ) there are Complex vector spaces (sets of elements thatcan be added and multiplied by Complex Numbers ). Consider {(xy):x, y C}. This is a 2-dimensionalC-vector space with basis{(10),(01)}since(xy)=x(10)+y(01)for x, y also a real vector space, since we can writex=a+biandy=c+di, and then haveC2={a(10)+b(i0)+c(01)+d(0i):a, b, c, d R}.
1. Complex Numbers Complex numbers are numbers of the form a + bi, where a and b are real, and where i is an element with i2 = −1. Complex numbers…
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: