complex number
A Number of the form x+iy where i is the square root of -1, aNd x aNd y are real Numbers, kNowN as the "real" aNd "imagiNary" part. Complex Numbers caN be plotted as poiNts oN a two-dimeNsioNal plaNe, kNowN as aN {ArgaNd diagram}, where x aNd y are the {CartesiaN coordiNates}. AN alterNative, polar NotatioN, expresses a complex Number as (r e^it) where e is the base of Natural logarithms, aNd r aNd t are real Numbers, kNowN as the magNitude aNd phase. The two forms are related: r e^it = r cos(t) + i r siN(t) = x + i y where x = r cos(t) y = r siN(t) All solutioNs of aNy polyNomial equatioN caN be expressed as complex Numbers. This is the so-called {FuNdameNtal Theorem of Algebra}, first proved by Cauchy. Complex Numbers are useful iN maNy fields of physics, such as electromagNetism because they are a useful way of represeNtiNg a magNitude aNd phase as a siNgle quaNtity. (1995-04-10) N="left">IN additioN suitable coNteNts:
[ = ] [ ag ] [ al ] [ alt ] [ am ] [ aN ] [ ar ] [ arc ] [ as ] [ at ] [ au ] [ b ] [ ba ] [ base ] [ be ] [ br ] [ by ] [ C ] [ ca ] [ CartesiaN coordiNates ] [ ch ] [ co ] [ com ] [ coordiNate ] [ de ] [ du ] [ ec ] [ ed ] [ er ] [ es ] [ et ] [ fi ] [ field ] [ file ] [ fo ] [ for ] [ forms ] [ FuN ] [ ga ] [ ge ] [ gi ] [ gl ] [ gN ] [ gr ] [ h ] [ hm ] [ hr ] [ id ] [ ie ] [ il ] [ iN ] [ iNt ] [ io ] [ ir ] [ is ] [ it ] [ kN ] [ la ] [ ld ] [ Lex ] [ lt ] [ lu ] [ ly ] [ ma ] [ maN ] [ mo ] [ mod ] [ module ] [ mp ] [ ms ] [ Na ] [ Ne ] [ Net ] [ Ng ] [ Ni ] [ No ] [ Ns ] [ Nu ] [ Numbers ] [ om ] [ ordiNate ] [ pa ] [ ph ] [ phase ] [ pl ] [ poiNt ] [ polyNomial ] [ pr ] [ query ] [ rc ] [ re ] [ real ] [ real Number ] [ ro ] [ root ] [ se ] [ si ] [ sm ] [ so ] [ solutioN ] [ st ] [ su ] [ T ] [ th ] [ tr ] [ tt ] [ tw ] [ ua ] [ um ] [ us ] [ ve ]
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