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) 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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