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| {{multiple issues|
| | The writer is called Wilber Pegues. Invoicing is my occupation. My spouse and I reside in Mississippi but now I'm contemplating other options. She is truly fond of caving but she doesn't have the time recently.<br><br>Also visit my webpage :: authentic psychic readings ([http://www.taehyuna.net/xe/?document_srl=78721 www.taehyuna.net]) |
| {{Cleanup|date=June 2010}}
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| {{Unreferenced|date=November 2006}}
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| In [[geometry]], an '''imaginary line''' is a [[line (mathematics)|straight line]] that only contains one [[real point]]. It can be proven that this point is the intersection point with the [[conjugated line]].
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| It is a special case of an [[imaginary curve]].
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| It can be proven that there exists no equation of the form <math>ax+by+cz=0</math> in which a, b and c are all [[real number|real]] coefficients. However there do exist equations of the form <math>ax+by+cz=0</math>, but at least one of the coefficients need be [[Complex number|nonreal]].
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| As follows, it can be proven that, if an equation of the form <math>ax+by+cz=0</math> in which a, b and c are all real coefficients, exist, the straight line is a [[real line]], and it shall contain an infinite number of real points.
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| This property of straight lines in the [[complex projective plane]] is a direct consequence of the [[duality (mathematics)|duality principle]] in [[projective geometry]].
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| In the [[complex plane]] (Argand Plane), we have a term called "imaginary axis".In Argand plane, y-axis is imaginary axis. All numbers in this axis are in form of 0+ib form.
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| == Argument ==
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| An argument is the angle or projection of any [[complex number]] in the Argand plane on the real axis (x-axis), denoted Arg(z). The argument can be easily found by following procedure:
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| If a+ib is any complex number foming angle A on real axis then,
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| cosA = a/√a^2+b^2 sinA= b/√a^2+b^2 tanA=b/a
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| arg(z)=A
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| == Properties of argument ==
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| * arg(AxB)=arg(A) + arg(B)
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| * arg(A/B)=arg(A) - arg(B)
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| * arg(z)=0 [[if and only if]] z lies in +ve real axis
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| * arg(z)=180 if and only if z lies in -ve real axis
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| * arg(z)=90 if and only if z lies in +ve imaginary axis
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| * arg(z)=-90 if and only if z lies in -ve imaginary line
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| * arg(z) lies in (0,90) in first quadrant, in (90,180) in 2nd quadrant, in(-180,-90) in 3rd quadrant, in(-90,0) in 4th quadrant.
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| [[Domain of a function|Domain]] of argument = R
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| [[Range (mathematics)|Range]] = (-180,180)
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| == Modulus == | |
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| Modulus of any complex no. a+ib is
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| mod(z)=√a^2+b^2
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| In Argand plane, [[Absolute value|modulus]] denotes distance between a complex number and the origin (0,0).
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| Example:
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| mod(z)=2 denotes [[locus (mathematics)|locus]] of all complex numbers z lying in circle of radius 2 at centre (0,0)
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| ==See also==
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| *[[Imaginary point]]
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| *[[Real curve]]
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| *[[Conic sections]]
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| *[[Complex geometry]]
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| *[[Imaginary number]]
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| {{DEFAULTSORT:Imaginary Line (Mathematics)}}
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| [[Category:Projective geometry]]
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The writer is called Wilber Pegues. Invoicing is my occupation. My spouse and I reside in Mississippi but now I'm contemplating other options. She is truly fond of caving but she doesn't have the time recently.
Also visit my webpage :: authentic psychic readings (www.taehyuna.net)