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Post by speakertoanimals on Feb 10, 2011 12:43:45 GMT 1
Well, doesn't mean much unless you put the brackets in:
(-1)^0.5
in which case it means the same as sqrt(-1).
And what does that mean? What you thoughtit means, a number which when squared yields the result -1.
It obviously can't be an ordinary number, becase all positive and negative real numbers square to give a positive result.
Hence we need to extend the numbers to the complex numbers, and we just add i, sqrt(-1).
Although we could go further than that, but I'll leave quaternions to a later date.....................
To do complex arithmetic, we just need to know that they add and multiply as you might expect.
It's not such a case of what does i mean, but what it is DEFINED to be (and is your definition consistent). It is, so job done.
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Post by carnyx on Feb 10, 2011 12:57:40 GMT 1
More "Woof! Woof!"
Wronnnnggggg ....
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Post by Progenitor A on Feb 10, 2011 13:03:56 GMT 1
Ok, let's talk about -1 0.5. What precisely does this mean? Come to that, what is  -1? Well, it is an imaginary number it does not exist outside the mind, (but then, does any number exist outside the mind) But this imgainary number has magical properties. It allows the solution of equations involving the nth root to be solved (that cannot be solved without it), it rotates vectors by multiples of 90 degrees in an Argand diagram, it brings elegance to mathematics eliminating ugly trig identities such SinASinB-CosACosB. In electrical engineering some problems are insoluble without its use and it has a very , very strange life of its own as Mandelbrot discovered. And Penrose uses it to explain the two-slit phenomenon Don't call me on the latter, I will call you |
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Post by abacus9900 on Feb 10, 2011 13:12:53 GMT 1
Well, doesn't mean much unless you put the brackets in: (-1)^0.5 in which case it means the same as sqrt(-1). And what does that mean? What you thoughtit means, a number which when squared yields the result -1. It obviously can't be an ordinary number, becase all positive and negative real numbers square to give a positive result. Hence we need to extend the numbers to the complex numbers, and we just add i, sqrt(-1). Although we could go further than that, but I'll leave quaternions to a later date..................... To do complex arithmetic, we just need to know that they add and multiply as you might expect. It's not such a case of what does i mean, but what it is DEFINED to be (and is your definition consistent). It is, so job done. Ok, good, I've got that. What's next? |
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Post by abacus9900 on Feb 10, 2011 13:30:15 GMT 1
Cheer up Abacus9900. Why the sad face? It's Thursday tomorrow and that's nearly the weekend......or don't you do weekends. I have all the kids from school for a science club on Saturday mornings. We make stuff like comets out of dry ice and charcoal and we talk about how things change, Liebnitz described it, he called it calculus. Newton preferred fluxions. What ever, it's an abstraction, electricity and music can be described by it. These kids are 16 and they understand maths, come to my class Abacuss, every Saturday morning at 10am, you will learn more here than anywhere. Thank you but might look a bit suspicious a grown man being with a group of 16 y.o.  |
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Post by speakertoanimals on Feb 10, 2011 14:14:10 GMT 1
Don't let the imaginary get you all heated about it not existing outside the mind! That's just more of your uusal silliness. DItto the maths is just a representation of the real world, same tired ole nonsense............
Carnyx seems to think this is worth barking at. God knows why, because the rules for complex arithmetic are so simple even he should be able to use them!
So, if (a+ib) is a complex number (real part and imaginary part), and (c+id) is another, you just add and multiply as you might expect, you just have to remember that i squared gives you minus one. There is no special rule to do complex arithmetic, so I have no idea why Carnyx seems to have transmuted into the dog-faced boy.....................
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Post by abacus9900 on Feb 10, 2011 15:25:17 GMT 1
Don't let the imaginary get you all heated about it not existing outside the mind! That's just more of your uusal silliness. DItto the maths is just a representation of the real world, same tired ole nonsense............ Carnyx seems to think this is worth barking at. God knows why, because the rules for complex arithmetic are so simple even he should be able to use them! So, if (a+ib) is a complex number (real part and imaginary part), and (c+id) is another, you just add and multiply as you might expect, you just have to remember that i squared gives you minus one. There is no special rule to do complex arithmetic, so I have no idea why Carnyx seems to have transmuted into the dog-faced boy..................... Ok let me check my understanding. Let's take an example of addition: (5+i2) + (3+i3) = 8 (real part) + i5 (imaginary part). = 8 + i5 Ans. Correct? What about multiplication? |
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Post by speakertoanimals on Feb 10, 2011 15:33:01 GMT 1
Just multiply out the brackeys as you would normally.
So, whether it was complex numbers or not, you'd say that:
a(b+ic) = ab + iac and so on. You just mutiply up the parts you can (like 3x2 or ixi), and leave the rest alone.
But I don't believe for a MINUTE that you actually don't, know this abacus, so why keep wasting our time?
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Post by Progenitor A on Feb 10, 2011 15:53:57 GMT 1
Feel free to 'waste' my time Abacus!
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Post by abacus9900 on Feb 10, 2011 18:22:38 GMT 1
Feel free to 'waste' my time Abacus! Ok, what about division? (STA seems a bit hostile at the moment). |
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Post by Progenitor A on Feb 10, 2011 18:45:49 GMT 1
Feel free to 'waste' my time Abacus! Ok, what about division? (STA seems a bit hostile at the moment). Ah! A bit more difficult Lets try 2 + 3j/4 +3j............................(i) To do this we take the conjugate of 4 + 3j The conjugate of 4 +3j = 4 -3j Lets multiply ...(i) by theis conjugate: (2 + 3j)(4 - 3j)/(4 + 3j)(4 - 3j) Top line (2 + 3j)(4 - 3j)= ( 8 + 6j + 12j + 9j 2) = (8 +18j -9) = -1 + 18j Bottom Line (4 + 3j)(4 - 3j) = 16 - 12j + 12j + 9 =25 Combining Top and bottom lines -1 + 18j/25 Therefore: 2 + 3j/4 +3j = -1 + 18j/25 = -1/25 + j18/25 So to divide, we multiply top and bottom by the complex conjugate of the denominator. |
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Post by abacus9900 on Feb 10, 2011 20:48:30 GMT 1
conjugate?  |
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Post by Progenitor A on Feb 10, 2011 21:34:43 GMT 1
conjugate? Two complex numbers that are identical except in the sign of the imaginary part |
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Post by robinpike on Feb 11, 2011 15:21:46 GMT 1
Maths goes further, maths is a science, it's abstract, like love and hate, it lives in the mind. Physics is real, it's about what stuff does but it can't be fully described without maths, neither can biology or chemistry..why do you have such a problem with this? Yes, but maths is just a tool, it is only useful if it is applied (and valued) in an appropriate way. For example, the theory of relativity does not include what electrons and protons are, so using maths in this instance is a summary of how to calculate what those things do, without explaining how they do it. You need a non mathematical description of the electron and proton to reveal that - which typically means a pictorial description. |
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Post by robinpike on Feb 11, 2011 15:25:41 GMT 1
It just does, get used to quantum theory, and stop wasting everyones time with these inane posts. STA, that a single photon 'goes both ways' through the two slits is a deduction, it is not as such a fact, and therefore could be wrong. |
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