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Topic: Imaginary part

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Complex number

Complex number

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	Introduction to the Mandelbrot Set
		However, first we have to find many numbers that are part of the set.
		As we test many complex numbers we can graph the ones that are part of the Mandelbrot set on the complex number plane.
		Not only do colors enhance the image aesthetically, they help to highlight parts of the Mandelbrot set that are too small to show up in the graph.
	www.olympus.net /personal/dewey/mandelbrot.html (955 words)

	[No title]
		The surface is colored according to the imaginary part.
		The right graphic is a contour plot of the scaled imaginary part, meaning the height values of the left graphic translate into color values in the right graphic.
		The right graphic is a contour plot of the scaled absolute value of the imaginary part, meaning the height values of the left graphic translate into color values in the right graphic.
	functions.wolfram.com /ElementaryFunctions/ArcCot/visualizations/5.html (983 words)

	Imaginary number Summary
		Although Descartes originally used the term "imaginary number" to mean what is currently meant by the term "complex number", the term "imaginary number" today usually means a complex number with a real part equal to 0, that is, a number of the form bi.
		Geometrically, imaginary numbers are found on the vertical axis of the complex number plane, allowing them to be presented orthogonal to the real axis.
		Imaginary numbers have essential concrete applications in a variety of sciences and related areas such as signal processing, control theory, electromagnetism, quantum mechanics, and cartography.
	www.bookrags.com /Imaginary_number (1323 words)

	Imaginary number - Wikipedia, the free encyclopedia
		In mathematics, an imaginary number (or purely imaginary number) is a complex number whose square is a negative real number or zero.
		Although Descartes originally used the term "imaginary number" to mean what is currently meant by the term "complex number", the term "imaginary number" today usually means a complex number with a real part equal to 0, that is, a number of the form i y.
		In electrical engineering and related fields, the imaginary unit is often written as j to avoid confusion with a changing current, traditionally denoted by i.
	en.wikipedia.org /wiki/Imaginary_number (920 words)

	Complex Numbers for AC Circuits Analysis
		Both the real and imaginary parts are real numbers, but the imaginary part is multiplied with the square root of -1.
		The complex conjugate of a number is the number that has the same real part as the original number but an imaginary part that differs only in its sign.
		If you look at the real and imaginary parts of a complex number as coordinates in a plane, then the real part would be the x coordinate and the imaginary part the y coordinate.
	www.circuit-magic.com /complex_numbers.htm (713 words)

	Algebraic Techinques - Complex Numbers
		The conjugate of a complex number is the complex number having the same real part, but whose imaginary part is the additive inverse of the former.
		Since the imaginary part of a real number is zero, the conjugate of a real number is simply the real number itself.
		In the multiplication of complex numbers, the distributive property is applied to the real and imaginary parts of the complex numbers.
	library.thinkquest.org /10030/4complex.htm (583 words)

	PlanetMath: complex
		Using this representation, we see that the real numbers are located at the abscissa (horizontal) axis, which is then known as the real axis.
		The ordinate (vertical) axis is known as the imaginary axis, since it consists of all complex numbers with real part equal to zero.
		See Also: polynomial, Argand diagram, real number, complex number, complex conjugate, nth root, Riemann zeta function, imaginary, imaginary unit, region, unit disk, upper half plane, zeroes of analytic functions are isolated, Riemann sphere, square root, Cardano's formulae, fundamental theorem of algebra,
	planetmath.org /encyclopedia/RealPart2.html (390 words)

	imaginary part - Search Results - MSN Encarta
		- part of complex number: the real number, b, in the complex number a + ib, where i is the square root of minus one
		Cure, The (rock band), English rock band formed in 1976, part of the goth pop scene and enduringly popular with fans.
		Goldwynisms: I read part of it…, Management: I tell you, the only…, Philosophy: The value of a whole must not be assumed to…, Proverbs: If a woman...
	encarta.msn.com /imaginary+part.html (173 words)

	RC Low Pass Transfer Function Computations
		Using this array as the input, the real and imaginary parts shown in Figure 3 are the complex output of an FFT routine.
		Although both the real and imaginary parts of the FFT have symmetries, the exact form seems not the match the Hermitian symmetry given by Equations 1 and 2.
		Figure 10 The real part (upper panel) and imaginary part (lower panel) for the two square pulse input converted to the frequency domain with an FFT and then unwrapped in frequency.
	www.jsu.edu /depart/psychology/sebac/low-pass (3385 words)

	Refractive index
		The real part of this number is the "ordinary" refractive index as discussed above, whilst the imaginary part indicates the amount of absorption.
		Note that the real part of the refractive index has been calculated using the IAPWS method for 5 C, whereas the imaginary part has been interpolated from Pope and Fry' s data.
		When using the IAPWS values for the real part of the refractive index, MiePlot uses the Pope and Fry data for the imaginary part in the visible spectrum because this data source is considered by Piotr Flatau to be the "most reliable".
	www.philiplaven.com /p20.html (755 words)

	Complex Diffusion Page
		The imaginary value serves as a robust edge-detector with increasing confidence in time, thus handles noise well and may serve as a controller for nonlinear processes.
		This is a natural regularized edge-detector (where edges are indicated by the zero-crossings of the imaginary part of the signal).
		Imaginary part kernel (bottom) approximates a second derivative of a Gaussian.
	www.math.ucla.edu /~gilboa/complex_diffusion_page.html (616 words)

	Ed Pizzi's Site - Mandelbrot and Julia Set Tutorial
		Imaginary numbers are usually taught first in a highschool Algebra II class, but anyone who has had any algebra at all should be able to understand this document.
		Along the real (horizontal) axis, you have the number line, as the imaginary parts of the numbers are zero.
		If you drew an imaginary vertical line between the point you want to evaluate to the x-axis and another from the point to the origin, you can use the triangle that is formed to determine the distance of the point from the origin, or from zero.
	www.patmedia.net /eaj.pizzi/docs/mandel.html (1382 words)

	CLHS: Function SINH, COSH, TANH, ASINH...
		The range is that strip of the complex plane containing numbers whose imaginary part is between -/2 and /2.
		A number with imaginary part equal to -/2 is in the range if and only if its real part is non-positive; a number with imaginary part equal to /2 is in the range if and only if its imaginary part is non-negative.
		A number with imaginary part equal to -/2 is in the range if and only if its real part is strictly negative; a number with imaginary part equal to /2 is in the range if and only if its imaginary part is strictly positive.
	www.lispworks.com /documentation/HyperSpec/Body/f_sinh_.htm (460 words)

	Imaginary part - Wikipedia, the free encyclopedia
		, the imaginary part of z is equal to
		, and hence that the imaginary part of re
		A load with purely imaginary current (such as a capacitor or inductor) dissipates no power; it merely accepts power temporarily then later pushes that power back on the power lines.
	en.wikipedia.org /wiki/Imaginary_part (214 words)

	Types of Numbers
		Imaginary numbers; that is, complex numbers with no real part.
		This imaginary number is equal to the square root of negative one.
		The real part is a, and b is called the imaginary part.
	id.mind.net /~zona/mmts/miscellaneousMath/typesOfNumbers/typesOfNumbers.html (433 words)

	AMTMP, theory
		are the changes in the real and the imaginary parts of dielectric constant; and K is a numerical factor that depends on the sample geometry.
		Thus in these general expressions, the change for both real and imaginary parts of dielectric constant depend on the cavity quality factor change and the shift of the resonance frequency.
		The real part is much greater than the imaginary part, and the change in the imaginary part is proportional to the change of the cavity quality factor while the change in the real part is proportional to the shift of the resonance frequency
	www.chembio.uoguelph.ca /serguei/theory.htm (950 words)

	Math Is Fun Forum / imaginary numbers
		Generally the portion bi would be ignored except when even powers of i appear, then portions of the imaginary part are added to the real part.
		All I said was a function that would return the real part of a complex number (Whether the imaginary coefficient is zero or not) so it can have a place value on the numberline.
		The imaginaries are not a field, a ring or even a group, as we agreed.
	www.mathsisfun.com /forum/viewtopic.php?pid=38894 (1265 words)

	Imaginary part in Ds
		The imaginary component ict in special relativity is just an artifact of the math chosen to work with the theory.
		There should be nothing philosophically interesting in why time is treated as an imaginary space coordinate, it's just something that comes with framing things a certain way.
		There is an analogy to be made with the imaginary numbers encountered in circuit diagrams and equations.
	www.physicsforums.com /showthread.php?t=3493 (1828 words)

	Complex numbers (Site not responding. Last check: )
		A complex number is the sum of a real number and a real multiple of the ``imaginary unit'' i, which is conventionally interpreted as the principal square root of -1.
		The abscissa and the ordinate are then referred to as the real part and the imaginary part of the complex number.
		The conjugate of a given complex number z is the complex number that has the same real part as z but a negated imaginary part.
	www.math.grin.edu /~stone/courses/fundamentals/complex-numbers.html (2008 words)

	CMPLX2I-Extracts the imaginary part of a complex data structure (Site not responding. Last check: )
		CMPLX2I creates a data structure, in which the data is taken from the imaginary part of a complex data structure.
		In the case of CMPLX2R it is the real part of the complex data that forms the data array in the resulting structure.
		For CMPLX2I, it is the imaginary part, and for CMPLX2M it is the modulus of the complex data.
	www.star.ucl.ac.uk /~mjc/figaro/sun86.htx/node233.html (329 words)

	ProSoundWeb \| The Nyquist Plot
		The Nyquist plot can be used in sound system work, where in acoustics the real part is particle pressure and the imaginary part is particle velocity (near a boundary or in a standing wave) and in impedance measurements where the real part is the resistance and the imaginary part is the reactance.
		The Nyquist plot, as embodied in contemporary acoustic analyzers, usually computes at the bottom of the screen the values for frequency, real part, imaginary part, phase, and magnitude for a given cursor position on the screen.
		Ron Bennett, a number of years ago, provided me with a program that allows acquisition of the real and imaginary part separately, i.e., acoustically as pressure and velocity: electrically as voltage and current; impedance as real and reactive.
	www.prosoundweb.com /install/sac/n26_4/nyquist/nyquist.shtml (707 words)

	sinh, cosh, tanh, asinh, acosh, atanh
		The range is that strip of the complex plane containing numbers whose imaginary part is between - pi /2 and pi /2.
		A number with imaginary part equal to - pi /2 is in the range if and only if its real part is non-positive; a number with imaginary part equal to pi /2 is in the range if and only if its imaginary part is non-negative.
		A number with imaginary part equal to - pi /2 is in the range if and only if its real part is strictly negative; a number with imaginary part equal to pi /2 is in the range if and only if its imaginary part is strictly positive.
	www.franz.com /support/documentation/6.2/ansicl/dictentr/sinhcosh.htm (427 words)

	Reflections on Thomas McGrath's Letter to an Imaginary Friend, Part One
		McGrath's Letter to an Imaginary Friend, Part One was such a book for me. It had a liberating effect on my writing and my understanding of ways to write poetry, and it helped me toward a deeper understanding of experience.
		Deriving in part from Whitman's collage technique in his long poem Song of Myself, McGrath's narrative sense of immediacy with historic events coupled with the struggle for self-knowledge diverges from Whitman's mystically Democratic personal and collective representation.
		Part of the tragedy of our time is that an obligation to such a sensibility has become unaccountable or indeterminate in the make up of human consciousness.
	www.pemmicanpress.com /articles/doren-robbins.html (3317 words)

	ComplexNumber
		Returns the imaginary part of the complex number.
		Sets the imaginary part of the complex number.
		A string which returns the real and imaginary parts of the complex number.
	www.duke.edu /~cwh9/assignments/javadoc/cn/Numbers/ComplexNumber.html (198 words)

	Fractal eXtreme: Fractal Theory
		Then we add up the imaginary parts which gives us 63i + 12i which is 75i.
		Z starts out being initialized to zero, that is, both the real and imaginary parts are set to zero.
		C is initialized to the complex number representing the point we want to calculate, its real portion is its horizontal distance from the centre of the plane, its imaginary portion is its vertical distance from the centre of the plane.
	www.cygnus-software.com /theory/theory.htm (1926 words)

	QuadtraticEquation
		The imaginary part of the first complex number.
		The imaginary part of the second complex number.
		The imaginary part of the third complex number.
	www.duke.edu /~tj10/code/javadoc/classwork/QuadtraticEquation.html (232 words)

	Complex and Imaginary Numbers
		At this point, our imaginary number may be starting to seem like a Pandora’s box.
		If a complex number's real part a equals 0—so it has the form bi for some real b—we say the number is purely imaginary (or, more simly, imaginary).
		If this were the case, we might feel compelled to extend the complex numbers through the addition of still another “imaginary” number to solve this new equation.
	www.riskglossary.com /articles/imaginary_numbers.htm (711 words)

	12.5.3. Branch Cuts, Principal Values, and Boundary Conditions in the Complex Plane
		Therefore the range of the one-argument logarithm function is that strip of the complex plane containing numbers with imaginary parts between -pi (exclusive) and pi (inclusive).
		A number with real part equal to zero is in the range if and only if its imaginary part is non-negative; a number with real part equal to pi is in the range if and only if its imaginary part is non-positive.
		Here is a sample of the PostScript code that generated figure 12-1, showing the initial scaling, translation, and clipping parameters; the code for one sector of the innermost annulus; and the code for the negative imaginary axis.
	www.cs.cmu.edu /Groups/AI/html/cltl/clm/node129.html (3105 words)

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