For negative numbers you'll only run into trouble with even roots. Besides (-1)^(1/2) is defined, as i.
Computer Science Canada What does this equal to? |
| Author: | SJ [ Fri Apr 17, 2009 4:16 pm ] |
| Post subject: | What does this equal to? |
(-1) ^ (2/3) interesting enough, when i asked 2 friends today, they responded simultaneously, one said "1" and one said "undefined". so is it ( (-1) ^ (2) ) ^ (1/3) or ( (-1) ^ (1/3) ) ^ 2 ? |
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| Author: | OneOffDriveByPoster [ Fri Apr 17, 2009 4:25 pm ] |
| Post subject: | Re: What does this equal to? |
SJ @ Fri Apr 17, 2009 4:16 pm wrote: so is it ( (-1) ^ (2) ) ^ (1/3) or ( (-1) ^ (1/3) ) ^ 2 ? It doesn't matter:
( (-1) ^ 2 ) ^ (1/3) = 1 ^ (1/3) = 1 ( (-1) ^ (1/3) ) ^ 2 = (-1) ^ 2 = 1 |
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| Author: | [Gandalf] [ Fri Apr 17, 2009 4:36 pm ] |
| Post subject: | RE:What does this equal to? |
For negative numbers you'll only run into trouble with even roots. Besides (-1)^(1/2) is defined, as i. |
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| Author: | endless [ Fri Apr 17, 2009 4:39 pm ] |
| Post subject: | RE:What does this equal to? |
http://www.google.ca/search?hl=en&safe=off&q=%28-1%29%5E%282%2F3%29&btnG=Search&meta= |
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| Author: | SJ [ Fri Apr 17, 2009 6:03 pm ] |
| Post subject: | RE:What does this equal to? |
ahh ok. thanks, i get it now. when i plug it into my calculator it gives me an error, so i guess it doesnt support imaginary numbers. though, i found out that if i graph y=x^(2/3) on graphmatica it's a cusp graph thats defined on both positive and negative sides. |
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| Author: | saltpro15 [ Fri Apr 17, 2009 6:13 pm ] |
| Post subject: | RE:What does this equal to? |
well, we can't argue with our Google overlords, that must be the correct solution! |
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| Author: | Brightguy [ Fri Apr 17, 2009 6:38 pm ] |
| Post subject: | Re: What does this equal to? |
OneOffDriveByPoster @ Fri Apr 17, 2009 4:25 pm wrote: It doesn't matter:
( (-1) ^ 2 ) ^ (1/3) = 1 ^ (1/3) = 1 ( (-1) ^ (1/3) ) ^ 2 = (-1) ^ 2 = 1 This isn't using the principal value, though; Google is correct if you want that. This came up two years ago [my post is basically unreadable since LaTeX broke  ]. |
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| Author: | zero-impact [ Fri Apr 17, 2009 6:42 pm ] |
| Post subject: | RE:What does this equal to? |
On a similiar note. Today I was playing with imaginary numbers and came up with this 
Where did I go horribly wrong?? |
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| Author: | apomb [ Fri Apr 17, 2009 8:03 pm ] |
| Post subject: | Re: RE:What does this equal to? |
zero-impact @ Fri Apr 17, 2009 6:42 pm wrote: On a similiar note. Today I was playing with imaginary numbers and came up with this
Where did I go horribly wrong?? because (-1)(-1) ≠ √1 well... maybe i guess it does |
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| Author: | CodeMonkey2000 [ Fri Apr 17, 2009 8:35 pm ] |
| Post subject: | RE:What does this equal to? |
√1 =+/- 1 There are 2 answers. |
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| Author: | zero-impact [ Fri Apr 17, 2009 9:22 pm ] |
| Post subject: | RE:What does this equal to? |
does that not still mean that 1 can equal -1 or +1? |
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| Author: | CodeMonkey2000 [ Fri Apr 17, 2009 9:24 pm ] |
| Post subject: | RE:What does this equal to? |
What? How did you come to that conclusion? √1 =+/- 1 You ignored the second root in your series of equations, so the whole thing is flawed. |
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| Author: | zero-impact [ Fri Apr 17, 2009 10:04 pm ] |
| Post subject: | RE:What does this equal to? |
I understand what you are saying now. I knew it was flawed, I was simply asking how. Thank you. |
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| Author: | Brightguy [ Sat Apr 18, 2009 12:23 am ] |
| Post subject: | Re: What does this equal to? |
CodeMonkey2000 @ Fri Apr 17, 2009 8:35 pm wrote: There are 2 answers.
This also came up before. Any nonzero number has two distinct square roots, but the standard is √ denotes a function, so it is single-valued and defined to be the principal square root. The real problem is that (a*b)^c = (a^c)*(b^c) doesn't always hold. It does hold when a, b have positive real part or when c is an integer (of course ab must be nonzero). Again we are using the principal value (otherwise a^b for irrational b would have an infinite number of values, for example). |
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| Author: | endless [ Sat Apr 18, 2009 7:00 am ] |
| Post subject: | Re: What does this equal to? |
Brightguy @ Sat Apr 18, 2009 12:23 am wrote:
ha, reading through that thread is hilarious. |
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