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Topic: Imaginary number

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	Imaginary number - Wikipedia, the free encyclopedia
		Imaginary numbers were defined in 1572 by Rafael Bombelli.
		One way of viewing imaginary numbers is to consider a standard number line, positively increasing in magnitude to the right, and negatively increasing in magnitude to the left.
		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.
	en.wikipedia.org /wiki/Imaginary_number (787 words)

	Number - Simple English Wikipedia
		A number can be a symbol (such as 1, 2, 3,...) or a word (such as one, two, three,...) used for counting and for doing mathematical calculations.
		Integers are all the positive numbers, all the negative numbers, and the number zero.
		This number is the square root of minus one (-1).
	simple.wikipedia.org /wiki/Number (1173 words)

	Imaginary part - Wikipedia, the free encyclopedia
		In mathematics, the imaginary part of a complex number z, is the second element of the ordered pair of real numbers representing z, i.e.
		The complex function which maps z to the imaginary part of z is not holomorphic.
		The "imaginary current" y is related to the current when the voltage is zero.
	en.wikipedia.org /wiki/Imaginary_part (270 words)

	Imaginary number (Site not responding. Last check: 2007-08-19)
		In mathematics an imaginary number (or purely imaginary number) is a complex number whose square is negative or zero.
		One way of viewing imaginary numbers is consider a standard number line positively increasing in magnitude to the and negatively increasing in magnitude to the At zero on this x axis draw a y axis; "positive" imaginary numbers then increase magnitude upwards and "negative" imaginary numbers increase magnitude downwards.
		For human tasks real numbers (or even rational offer an adequate description of data and numbers have no meaning; however in many of science and mathematics imaginary numbers (and numbers in general) are essential for describing Imaginary numbers have essential concrete applications in variety of sciences and related areas such electromagnetism quantum mechanics and cartography.
	www.freeglossary.com /Imaginary_number (637 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-08-19)
		A complex number is written as a + ib, where i is the imaginary unit (the square root of - 1), and a and b are real numbers.
		An imaginary number is one where the real part (the "a") is zero, so an imaginary number is written as just ib, where b is a real number.
		Thus, every complex number is associated with a point in the xy plane, and every point in the xy plane is associated with a complex number.
	mathforum.org /library/drmath/view/53810.html (560 words)

	Math Forum: Ask Dr. Math FAQ: Imaginary Numbers
		Contrary to what some people might tell you, imaginary numbers are not numbers that only exist in the brains of weird people.
		Imaginary numbers are numbers that can be written as a real number times i.
		actually, there are TWO numbers that are the square root of -1, and those numbers are i and -i, just as there are two numbers that are the square root of 4, 2 and -2.
	mathforum.org /dr.math/faq/faq.imag.num.html (340 words)

	Imaginary Numbers
		Imaginary numbers are an intriguing artifact of negative numbers.
		When negative numbers are multiplied, we are given certain rules for the operation: (1) When two positive numbers are multiplied, the result is positive; (2) when two negative numbers are multiplied, the result is also positive; and (3) when a negative and a positive number are multiplied, the result is negative.
		The conjugate axis of a hyperbola is, in a sense, an imaginary measurement.
	www.friesian.com /imagine.htm (4918 words)

	PlanetMath: imaginary
		A complex number is called imaginary if its real part is 0.
		Note that the imaginary numbers are closed under addition but not under multiplication, since
		This is version 5 of imaginary, born on 2002-02-16, modified 2005-01-21.
	planetmath.org /encyclopedia/Imaginary.html (114 words)

	Lesson Page - Imaginary Unit
		The reason for the name "imaginary" numbers is that when these numbers were first proposed several hundred years ago, people could not "imagine" such a number.
		It is said that the term "imaginary" was coined by René Descartes in the seventeenth century and was meant to be a derogatory reference since, obviously, such numbers did not exist.
		An imaginary number is a number whose square is negative.
	regentsprep.org /Regents/mathb/2c2/imagineLes.htm (111 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.
		A Complex Numbers is a combination of a real number and an imaginary number in the form a + bi.
	id.mind.net /~zona/mmts/miscellaneousMath/typesOfNumbers/typesOfNumbers.html (433 words)

	imaginary number
		Every imaginary number can be written in the form ib where b is a real number and i the imaginary unit with the property that i
		Imaginary numbers are complex numbers in which the real part is zero.
		The term "imaginary" is unfortunate because it suggests something that has less reality than a "real" number, which isn't the case.
	www.daviddarling.info /encyclopedia/I/imaginary_number.html (131 words)

	Is Time The Imaginary Number? - Unexplained Mysteries Discussion Forums
		Current is plotted horizontally on a graph and an imaginary vertical axis is used for j; a2 +b2 = c2 pythagorean theorem is used to calculate a value for the current.
		The imaginary number, used in calculating current and other things, has an imaginary axis on a graph that is at a right angle to the real axis, and it is therfore acting as a 4th dimension.
		Topics utilizing complex numbers include the investigation of electrical current, wavelength, liquid flow in relation to obstacles, analysis of stress on beams, the movement of shock absorbers in cars, the study of resonance of structures, the design of dynamos and electric motors, and the manipulation of large matrices used in modeling.
	www.unexplained-mysteries.com /forum/index.php?showtopic=57685&st=0& (1995 words)

	Imaginary Numbers - Search Results - MSN Encarta (Site not responding. Last check: 2007-08-19)
		Imaginary Numbers, numbers formed by multiplying a real number times i, where i is the square root of minus 1.
		An imaginary number is a multiple of i, where i is the square...
		Number (mathematics), word or symbol used to designate quantities or entities that behave like quantities.
	encarta.msn.com /Imaginary_Numbers.html (149 words)

	Imaginary and Complex Numbers
		Mathematicians have designated a special number 'i' which is equal to the square root of minus 1.
		When a number has the form a + bi (a real number plus an imaginary number) it is called a "complex number".
		The main principle to remember in complex number division is that we multiply the "top" and "bottom" of the fraction by the conjugate of the denominator.
	www.1728.com /compnum2.htm (480 words)

	[No title]
		Recall from your algebra days that a complex number is one that can be written in the form a + bi, where a and b are real numbers, and i represents the square root of -1.
		That is the real part of the sum of two complexes is the sum of their real parts, and the imaginary part of the sum of two complexes is the sum of their imaginary parts.
		Conjugation: The conjugate of the complex number a + bi is defined to be the complex number a — bi.
	www.richmond.edu /~dszajda/classes/cs150/Fall_2003/labs/October17/instructions.doc (519 words)

	imaginary number - a definition from Whatis.com
		- An imaginary number is a quantity of the form ix, where x is a real number and i is the positive square root of -1.
		The set I of imaginary numbers consists of the set of all possible products iw, where w is an element of the set R of real numbers.
		Imaginary and complex numbers are used in engineering, particularly in electronics.
	searchsmb.techtarget.com /sDefinition/0,,sid44_gci283974,00.html (314 words)

	BBC - Radio 4 - 5 Numbers - The Imaginary Number
		The imaginary number is the square root of -1 and is known as 'i'.
		Imaginary numbers are real numbers multiplied by i.
		Imaginary time is measured in imaginary numbers and unlike real time, it can move backwards and forwards like an extra spatial dimension.
	www.bbc.co.uk /radio4/science/5numbers4.shtml (419 words)

	Imaginary Numbers Are Not Imaginary.
		A number is not the written symbol like "5" or the written word "five," it is the idea that is symbolized by "5" or "five." It's something intangible.
		With these numbers, one can't express as a single number the "number whose square is 27" or the "number whose cube is 16" even though one could express the "number whose cube is 27" or the "number whose square is 16." Irrational numbers are needed.
		The square root of negative four is imaginary in the math sense, meaning a multiple of the square root of negative one.
	www.mathnstuff.com /math/spoken/here/3essay/eimage.htm (821 words)

	Complex and Imaginary Numbers
		Similarly, we may have a mathematical problem that is expressed entirely with real numbers and has a solution that depends only on real numbers.
		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)

	What's a number?
		Given the difficulty of establishing whether a given number is algebraic or not, this was one of Cantor's early surprising results.
		The rest of the complex numbers could also be defined by adding this new number i to the set of reals and postulating that usual arithmetic operations (addition, subtraction, multiplication) apply to the expanded set and all the laws known to hold for these operations hold for the new set as well.
		The rest of surreal numbers (included are the numbers we discussed so far and myriads of numbers some of which I have a difficulty imagining.) are formed starting with 0 and applying just two simple rules.
	www.cut-the-knot.org /do_you_know/numbers.shtml (3546 words)

	Introduction to angles
		The number b is sometimes referred to as the coefficient of i.
		Division of complex numbers is the most complicated of the four basic arithmetic operations.
		To divide a complex number by another complex number, multiply the numerator and the denominator by the complex conjugate of the denominator.
	colalg.math.csusb.edu /CAMDEMO/coordinateplane/src/complex.html (447 words)

	2.3 - Complex Numbers (Site not responding. Last check: 2007-08-19)
		If two complex numbers are equal, then the real component of the left side must equal the real component of the right side and the imaginary component of the left side must equal the imaginary component of the right side.
		To eliminate the imaginary component from a complex number, multiply by its complex conjugate.
		The numerator and denominator is multiplied by the complex conjugate of the denominator.
	www.richland.edu /james/lecture/m116/solutions/complex.html (404 words)

	Imaginary Numbers ........................................... (Site not responding. Last check: 2007-08-19)
		Numbers like this are called imaginary numbers, and they always involve the square root of a negative number.
		The problem with imaginary numbers really just arises from the negative under the root sign.
		Nevertheless, it is important to understand how complex numbers work, because some problems can be more easily solved by using imaginary solutions to guide us to the real ones.
	www.worsleyschool.net /science/files/sets/imaginary.html (374 words)

	Question Corner -- More Complex Number Questions
		That number will be purely real if the field is all electric with no magnetic component, purely imaginary if the field is all magnetic with no electric component, and in other cases will have a non-zero real part and a non-zero imaginary part.
		The number will be purely real if the medium affects the magnitude of the wave but leaves the phase unchanged, and purely imaginary if the medium shifts the phase by 90 degrees.
		That number will be purely real if there is a voltage across it but no current flowing through it (such as a fully charged capacitor) and purely imaginary if there is current flowing through it but no voltage across it (such as a fully discharged capacitor).
	www.math.toronto.edu /mathnet/questionCorner/complq.html (688 words)

	Sugarpacket: My imaginary number friend
		I haven't thought about imaginary numbers (represented by the little italic, lowercase "i") since my last math class in high school, precalculus and discrete math.
		A negative number multiplied by a negative number is always a positive number.
		Therefore, by definition of squaring a number, the square root of -16 is an imaginary number.)
	blogs.setonhill.edu /KarissaKilgore/009589.html (298 words)

	BBC - Radio 4 - 5 Numbers - Index
		Hear about the stark reality behind the imaginary number, try a slice of pi, find out about the natural beauty of the golden ratio, discover why some infinities are bigger than others, and see why nothing really matters.
		At its most complex, it is an irrational number that cannot be expressed as the ratio of two whole numbers and has a random decimal string of infinite length.
		Divide any number in the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55) by the one before it and the answer is always close to 1.618 the Golden Ratio.
	www.bbc.co.uk /radio4/science/5numbers.shtml (427 words)

	CBofN - Glossary - I
		Imaginary Number The square root of a negative number.
		Incomputable Number A real number with an infinite decimal (or binary) expansion that cannot be enumerated by any universal computer.
		While integration and differentiation are considered to be inverse operations, there are an infinite number of integrals that are valid results for integrating any function; thus, the process is not one-to-one.
	mitpress.mit.edu /books/FLAOH/cbnhtml/glossary-I.html (410 words)

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