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	Encyclopedia: Argand plane (Site not responding. Last check: 2007-10-19)
		It is to Argand's essay that the scientific foundation for the graphic representation of complex numbers is now generally referred.
		If the matrix is viewed as a transformation of a plane, then the transformation rotates points through an angle equal to the argument of the complex number and scales by a factor equal to the complex number's absolute value.
		The conjugate of the complex number z corresponds to the transformation which rotates through the same angle as z but in the opposite direction, and scales in the same manner as z; this can be described by the transpose of the matrix corresponding to z.
	www.nationmaster.com /encyclopedia/Argand-plane (2672 words)

	complex_plane (Site not responding. Last check: 2007-10-19)
		The complex plane is sometimes called the Argand plane or Gauss plane, and a...
		Complex plane This applet illustrates the complex plane (sometimes called the Argand plane in older books), which can be used to display complex numbers, in the same way the real line is used to...
		The complex plane has an important role in modern physics, and a great variety of problems in physics--both conceptual and technical--can be explored by using it.
	complex_plane.networklive.org /index.php?title=Complex_number&action=edit§ion=16 (321 words)

	Search Results for Argand
		Argand is famed for his geometrical interpretation of the complex numbers where i is interpreted as a rotation through 90 degrees.
		However, Argand was not a professional mathematician either, so when he published his geometrical interpretation of complex numbers in 1806 it was in a book which he published privately at his own expense.
		Argand was a man with an unknown background, a nonmathematical occupation, and an uncertain contact with the literature of his time who intuitively developed a critical idea for which the time was right.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?BIOGS=1&TOPICS=1&CURVES=1&REFS=1&BIBLI=1&SOCIETIES=1"=1&CHRON=1&WORD=Argand&CONTEXT=1 (1032 words)

	Complex Numbers - Complex Plane
		Since the description of complex numbers as points in the plane is often associated with the work of Carl Friedrich Gauss (1777-1855),
		is also sometimes referred to as the Argand plane; in this case, a plot of complex numbers is referred to as an Argand diagram.
		Similarly, it can be noticed that the number i corresponds to the point (0, i) in the complex plane and corresponds to the point (0, 1) in the Cartesian plane.
	collectiveknowledge.ucsc.edu /ComplexHistory/complexPlane.htm (473 words)

	Plane - Aircraft for sale: helicopters for sale, aircraft charter (Site not responding. Last check: 2007-10-19)
		Little Red Plane is a short animation done by a group of students from Art Center College Of Design.
		The complex plane is sometimes called the Argand plane or Gauss plane, and a plot of complex numbers in
		Sam the chameleon introduces graphing points on the numberline and the coordinate plane, for elementary and middle-school students.
	www.morepointer.com /mp/plane.html (235 words)

	Argand Diagrams (Site not responding. Last check: 2007-10-19)
		Argand diagrams are graphs with both a real and imaginary axis, the area covered by the diagram is known as the complex plane where any complex number can be represented by a point.
		The only problem that we may encounter when drawing Argand diagrams is when both a and b are negative and therefore (b/a) is positive.
		We must be aware of these cases and look out for them, the only way of getting around them is to find the angle and then use the signs of a and b to work out which quadrant should be used.
	students.bath.ac.uk /ma2laag/arganddiagrams.html (221 words)

	Argand Diagrams (Site not responding. Last check: 2007-10-19)
		argand diagrams make it easier to work out the arg as you can see which sector the complex number is in and therefore what numbers you have to use with arctan...
		This comes back to the argand diagram (as if it wasn't pretty enough), because the nth roots of 1 form pretty geometric shapes on the argand diagram.
		ANNNNNNND, the fact that the argand diagram is a plane which features all sorts of geometry makes it useful for other results which I haven't actually studied but have heard about.
	www.thestudentroom.co.uk /t51238.html (904 words)

	Math 132 Applet 1 (Site not responding. Last check: 2007-10-19)
		This applet illustrates the complex plane (sometimes called the Argand plane in older books), which can be used to display complex numbers, in the same way the real line is used to display real numbers.
		The red dot on the plane represents a complex number
		To test your knowledge of complex arithmetic, place the dot at a random location, select a random button, and see if you can predict where the dot is going to go.
	www.math.ucla.edu /~tao/java/Plane.html (152 words)

	Trigonometric function - Wikipedia, the free encyclopedia
		All triangles are taken to exist in the Euclidean plane so that the inside angles of each triangle sum to π radians (or 180°).
		The unit circle can be thought of as a way of looking at an infinite number of triangles by varying the lengths of their legs but keeping the lengths of their hypotenuses equal to 1.
		In this way, trigonometric functions become essential in the geometric interpretation of complex analysis.
	en.wikipedia.org /wiki/Trigonometric_function (3248 words)

	Complex numbers - Wikibooks
		Notice that this is a one-to-one relationship: for each complex number, we have one corresponding point in the plane, and for each point in the plane there corresponds one complex number.
		Notice that a purely imaginary number is represented in the Argand plane by a point on the imaginary axis.
		We are now able to calculate the modulus and argument of a complex number, where these two numbers are able to uniquely describe every number in the Argand plane.
	en.wikibooks.org /wiki/Calculus:Complex_analysis/Complex_Numbers (2124 words)

	How to Generate the Mandelbrot Set (Site not responding. Last check: 2007-10-19)
		Finally, the Argand plane is the way of representing complex numbers as points on a plane.
		To create the set, for each point in the plane, we use the algorithm I will describe below to determine if the point is in the set or not.
		If z remains close to the origin on the Argand plane, then it is a member of the mandelbrot set.
	www.maths.tcd.ie /~nryan/mandelbrot/how.html (471 words)

	Maybe this can forecast the market trend... best Gauss Plane (Site not responding. Last check: 2007-10-19)
		Unlike Gauss curvature, the mean curvature depends on the embedding, for instance, a cylinder and a plane are locally...
		Flow due to a plane scraping a plane for several scraping angles...
		Complex Plane -- from MathWorld Complex Plane -- from MathWorld The plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number.
	ascot.pl /th/Fourier4/Gauss-Plane.htm (534 words)

	Which Equation Explains the Market Cycle ? best Argand Plane (Site not responding. Last check: 2007-10-19)
		Argand Diagram -- from MathWorld Argand Diagram -- from MathWorld An Argand diagram is a plot of complex numbers as points z=x+iy in the complex plane using the x-axis as the real axis and y-axis as the imaginary axis.
		In this context it is called the Argand plane: to the complex...
		Argand diagrams can also be used with the modulus argument form...
	ascot.pl /th/Fourier1/Argand-Plane.htm (499 words)

	[No title]
		Imagine the complex plane flat on the ground, and imagine placing a sphere (of diameter 1) on the point with coordinates (0,0), corresponding to the number 0 + 0i = 0.
		It is found by connecting the point on the plane and the North pole of the sphere by a straight line.
		Seen on the plane, the modulus of a number is the distance of the corresponding point from the point Zero.
	www.dcs.gla.ac.uk /~bunkenba/CC/Macintosh/CC_user_manual (1878 words)

	Complex Numbers and Geometry
		It was not until Jean Robert Argand gave a concrete, geometric picture for this number, which related it to the "real" number line, that mathematicians began to accept i as more than a figment of their imagination, and started to refer to it as a "complex" number, after Gauss popularized the term.
		This picture was finally conceived, in 1806 by Jean Robert Argand, and is often called an "Argand diagram".
		The domain of both functions is equal to the complex plane, while their range is the real number line.
	campus.northpark.edu /math/PreCalculus/Transcendental/Trigonometric/Complex (2082 words)

	Introduction to DSP - IIR filters: IIR filter design by the bilinear transform
		The problem with which we are faced is to transform the analogue filter design into the sampled data z plane Argand diagram.
		The problem of aliasing arises because the frequency axis in the sampled data z plane Argand diagram is a circle:
		One way around this is to warp the analogue filter design before transforming it to the sampled data z plane Argand diagram: this warping being designed so that it will be exactly undone by the frequency warping later on.
	www.bores.com /courses/intro/iir/5_warp.htm (364 words)

	R c plane for sale
		As the web continues to gather r c plane for sale web pages, we will strive to deliver them to you.
		The best r c plane for sale tips may take a bit of time to spot.
		As r c plane for sale related topics continue to increase in popularity, there will be more places to learn more about this interesting matter.
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	The Argand Diagram (Site not responding. Last check: 2007-10-19)
		So it is often useful to think of a complex number as being represented by the point in a plane with Cartesian coordinates (x, y).
		This representation is called the Argand diagram or the complex plane.
		Figure 10.2: The Argand diagram or complex plane.
	www.maths.abdn.ac.uk /~igc/tch/eg1006/notes/node97.html (75 words)

	The Complex Plane (Site not responding. Last check: 2007-10-19)
		A complex number can be represented in the Complex Plane which may sometimes be referred to as the Argand Diagram.
		A complex plane is drawn just like any other plane, with two perpendicular axes.
		Below is one example of a complex number shown in the complex plane.
	www.bath.ac.uk /~ma2vt/Argand.html (120 words)

	Search Results for Complex
		There is a common belief that complex numbers are the end of the road in the development of numbers and Conway's discovery is the perfect illustration of how even the number systems are part of the continually evolving subject.
		By considering the action of the modular group on the complex plane, Klein showed that the fundamental region is moved around to tessellate the plane.
		On the theory of foci appeared in 1853 and it is one of his most important papers, investigating the angle between lines in the complex projective plane.
	www-history.mcs.st-and.ac.uk /Search/historysearch.cgi?SUGGESTION=Complex&CONTEXT=1 (12769 words)

	Module 7: Complex Numbers - Section 4
		This plane is often known as the "Argand diagram".
		This way of drawing complex numbers on a plane shouldn't seem so strange, since it is very like drawing points (x,y) in the xy-plane, using Cartesian coordinates, or like drawing vectors in the plane.
		If you are familiar with vectors (see the first-level module on vectors if you want to revise this topic) then you will remember that we can add vectors using their picture representation.
	www.es.ucl.ac.uk /undergrad/geomaths/7-com/cmn4.htm (692 words)

	Plane (Site not responding. Last check: 2007-10-19)
		It is impossible to pick random variables which are uniformly distributed in the plane (Eisenberg and Sullivan 1996).
		In 4-D, it is possible for four planes to intersect in exactly one point.
		Rigid motion of the hyperbolic plane is one of the previous types or a
	www.itu.dk /edu/documentation/mathworks/math/math/p/p339.htm (167 words)

	Locus/Regions in Argand Plane (Site not responding. Last check: 2007-10-19)
		Since any complex number z = x +iy corresponds to point (x,y) in complex plane (also called Argand plane), so many kinds of regions and geometric figures in this plane can be represented by complex equations or inequations.
		Illustrate the locus of z in the Argand plane.
		Illustrate the locus of z in the Argand diagram.
	www.ilovemaths.com /3argandplane.htm (686 words)

	Plane - The Canadian Galactic Plane Survey (Site not responding. Last check: 2007-10-19)
		Use the plane iron as a gauge to assure 1/16" adjustment clearance on center block.
		Oh my goodnessa definition: The inclined plane is a plane surface set at an angle, The inclined plane permits one to overcome a large resistance by
		Plane and Pilot Magazine is the first choice of general aviation pilots.
	www.yourwebfind.com /q/plane.html (406 words)

	Newton-Raphson Fractals (Site not responding. Last check: 2007-10-19)
		Suppose we take any complex number on the Argand plane as an initial guess at a root of this polynomial.
		For every point on the Argand plane we can find how long it takes for it to converge towards a root and which root that is. We can then colour the point accordingly.
		We can even choose where we want the roots located on the Argand plane, and construct a function therefrom.
	www.padre.ca /green/nrfract.php (283 words)

	A History of Hypercomplex Numbers (Site not responding. Last check: 2007-10-19)
		Jean Robert Argand (1768-1822) publishes an account of the graphical representation of complex numbers.
		Cauchy shows that an analytic function of a complex variable can be expanded about a point in a power series in the neighborhood of the singularity.
		He formulates a rigorous algebra of complex numbers based on the geometry of the complex plane.
	history.hyperjeff.net /hypercomplex.html (2046 words)

	Encyclopedia: Sine (Site not responding. Last check: 2007-10-19)
		They may be defined as ratios of two sides of a right triangle containing the angle, or, more generally, as ratios of coordinates of points on the unit circle, or, more generally still, as infinite series, or equally generally, as solutions of certain differential equations.
		In all of these cases referring to triangles, the triangles are taken to exist in the Euclidean plane, so that the angles always sum to 180°.
		For example, with the above identity, if one considers the unit circle in the Argand plane, defined by e
	www.nationmaster.com /encyclopedia/Sine (2904 words)

	Representations of complex numbers (Site not responding. Last check: 2007-10-19)
		The complex number z = x +iy can be uniquely represented by the point P(x, y) in the co-ordinate plane and conversely corresponding to the point P(x, y) in the plane there exists a unique complex number z = x +iy.
		The plane is called the complex plane and the representation of complex numbers as points in the plane is called Argand diagram.
		Show that the area of the triangle on the Argand plane formed by the complex numbers z, iz and z +iz is z²/2
	www.ilovemaths.com /3complex.htm (462 words)

	Constructing the Phase-space of the Scale-free Parcellular "Planck Oscillator" (Site not responding. Last check: 2007-10-19)
		Each parcellular state of this complex metaspace, represented by a vector in the Argand plane, will map conformally onto another by way of complex functions wherever the real component AB is non-zero.
		In other words in each case the orbit of the phase point projects from the plane to the line of the parcellular axis as a moving cursor that arbitrarily depicts AB or BA, being symmetrical with respect to these positive and negative directions.
		In this force case the lower bound of momentum in every direction is that of "true rest", and the asymmetry of inertia may increase in a reciprocal limit which, along any one dimension, is also just c, in which case the proper rest state of a node becomes as anisotropic as possible.
	www.parcellular.fsnet.co.uk /parc.mech.21.htm.htm (6306 words)

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