Quarta-feira, Janeiro 26, 2005
Um Aluno do 3º Ano de Engenharia não sabe o que é o "i"... a Entidade Imaginária!!!... PASME-SE!
Por favor não deixem o "futuro" Engenheiro vir a fazer ou a Engenhar: PONTES, Túneis, Constução Aeronáutica, Naval ou Espacial, Electrotecnia Alta e/ou Baixa, Telecomunicações, Contrução Cívil de qualquer Espécie, Rodoviária ou Ferroviária, Sistemas, Geográfica, Física,..., etc., etc.
Em Suma, Dêem-lhe já um Súbsidio de Desemprego Perene Mas Não o Deixem Mexer em Nenhum Engenho, nem nada, ou então Façam um Levantamento de Tudo Em Que Vier a Trabalhar ou Construir Neste Domínio ( Onde Como e Quando!).
Imaginary Number
In mathematics, an imaginary number (or purely imaginary number) is a complex number whose square is negative or zero. The term was coined by René Descartes in 1637 in his La Geometrie and was meant to be derogatory: obviously, such numbers were thought not to exist.
Definition:
http://en.wikipedia.org/math/9f7bfcfe543a38208ea1542aa31e23f7.png
Geometric Interpretation on Wikipedia
E (mathematical constant) - Wikipedia, the free encyclopedia
Definitions:
Properties:
The special case with x = π is known as Euler's identity:
Complex Number and History of Complex Numbers <<<<--- MUITO IMPORTANTE
Quaternion
Octonion
Imaginary numbers follow the same pattern. For most human tasks, real numbers (or even rational numbers) offer an adequate description of data, and imaginary numbers have no meaning; however, in many areas of science and mathematics, imaginary numbers (and complex numbers in general) are essential for describing reality. 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. They are absolutely indispensable in advanced mathematics.
In electrical engineering, when analyzing AC circuitry, the values for the electrical voltage (and current) are expressed as imaginary or complex numbers known as phasors. There is, however, nothing imaginary (in the non-mathematical sense) about these voltages and they can cause actual damage/harm to either humans or equipment even if their values contains no "real part".
Nota:
Definição: i=sqrt(-1)
Propriedades: i^2=-1, i^3=-i, i^4=1
Formas de Apresentação:
Rectangular ou Cartesina: a+bi, com a,b Pertencente ao corpo R (Real)
Trigonométrica: A*[cos(x)+isen(x)], "x" é Argumento Expresso em Radianos, logo x em R
Polar: A*e^ix, com e=2,71..., "e" número de Euller, Número Irracional proveniente da Expressão Limite e=lim(1+1/n)^n com n -> inf.
...
------------------------------------------- INC -------------------------------------------------------
Definitions:
Properties:
The special case with x = π is known as Euler's identity:
Complex Number and History of Complex Numbers <<<<--- MUITO IMPORTANTE
Quaternion
Octonion
Imaginary numbers follow the same pattern. For most human tasks, real numbers (or even rational numbers) offer an adequate description of data, and imaginary numbers have no meaning; however, in many areas of science and mathematics, imaginary numbers (and complex numbers in general) are essential for describing reality. 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. They are absolutely indispensable in advanced mathematics.
In electrical engineering, when analyzing AC circuitry, the values for the electrical voltage (and current) are expressed as imaginary or complex numbers known as phasors. There is, however, nothing imaginary (in the non-mathematical sense) about these voltages and they can cause actual damage/harm to either humans or equipment even if their values contains no "real part".
Nota:
Definição: i=sqrt(-1)
Propriedades: i^2=-1, i^3=-i, i^4=1
Formas de Apresentação:
Rectangular ou Cartesina: a+bi, com a,b Pertencente ao corpo R (Real)
Trigonométrica: A*[cos(x)+isen(x)], "x" é Argumento Expresso em Radianos, logo x em R
Polar: A*e^ix, com e=2,71..., "e" número de Euller, Número Irracional proveniente da Expressão Limite e=lim(1+1/n)^n com n -> inf.
...
------------------------------------------- INC -------------------------------------------------------
