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Post by Progenitor A on Sept 23, 2010 13:11:35 GMT 1
Hear the radio programe this morning?
Bit of a fuss really
We always chucked this away at school when we did quadratic equations
No bloody use you see.
But electricians and things use it!
Bloody rotate!
Well tha's what it does really.
Rotate
Multiply by -1exp0.5 and hey presto whatever you have got rotates 90 degrees
Some call it i, but electricians and things call it j 'cos they don't want to confuse it with i=instantaneous current.
So it has its uses.
It allows simplified maths for electricians
And , at school, if the answer had been £5i, then you just roate your five pound through 90 degrees!
Any other uses for this strange imaginary thing?
!Lots of things get thrown away in amths , don't they you know infinities and differential equation results that make no sense?)
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Post by abacus9900 on Sept 23, 2010 15:27:39 GMT 1
Quantum mechanics, cartography, electromagnetism, fluid dynamics, to name a few. In electrical engineering, an AC voltage has two parameters; the voltage potential and an angle called phase. So, an AC voltage could be said to have two dimensions which can be represented by a complex number which consists of an ordinary number and an imaginary number. Imagine a number line with origin 0. If you draw another line perpendicular to the ordinary number line through the origin (in other words at right angles to the ordinary number line) this represents the imaginary number line (denoted by y). Positive values appear above the origin 0 and negative ones below the origin. z denotes a complex number which consists of a 'real' part (x) and an 'imaginary' part (iy), which could be either positive or negative.  en.wikipedia.org/wiki/Imaginary_numberi raised to the power of 0 = 1; i raised to the power of 1 = i; i raised to the power of 2 = i x i = -1 (this is the definition of i, i.e. sqr. root of -1); i raised to the power of 3 = i x i x i = -1 x i = -i; i raised to the power of 4 = i x i x i x i = -1 x -1 = 1. The quick way to work out a given power of i with an exponent higher than 4 is to divide the exponent by 4 and whatever the remainder is equals one of the repeating exponents given above. For example, to work out what i^15 is, divide 15 by 4 and use the remainder to use as the exponent. So, 15/4 = 3 remainder 3, so the answer is i^3, = -i, and so on. Complex numbers are composed of a 'real' number and an 'imaginary' number. We can represent the real part as a and the imaginary part as b. Either of these can be 0. An example of a complex number is: -5 + 4i. Complex numbers are equal to one another when their real and imaginary numbers correspond. For example: a + bi = c + di when a = c and b =d. |
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Post by Progenitor A on Sept 23, 2010 15:42:18 GMT 1
Quantum mechanics, cartography, electromagnetism, fluid dynamics, to name a few. In electrical engineering, an AC voltage has two parameters - the voltage potential and an angle called phase. So, an AC voltage could be said to have two dimensions which can be represented by a complex number which consists of an ordinary number and an imaginary number. Imagine a number line with origin 0. If you draw another line perpendicular to the ordinary number line through the origin (in other words at right angles to the ordinary number line) this represents the imaginary number line (denoted by y). Positive values appear above the origin 0 and negative ones below the origin. en.wikipedia.org/wiki/Imaginary_numberThanks Abacus - I know I can count on you. I have some familiarity with operator j |
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Post by abacus9900 on Sept 23, 2010 15:55:41 GMT 1
No problem, naymissus, I enjoyed putting it together. I might even add more info to my original post.  |
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