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SJ

Fri Apr 17, 2009 4:16 pm


What does this equal to?

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(-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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OneOffDriveByPoster

Fri Apr 17, 2009 4:25 pm


Re: What does this equal to?

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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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[Gandalf]

Fri Apr 17, 2009 4:36 pm


RE:What does this equal to?

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For negative numbers you'll only run into trouble with even roots.  Besides (-1)^(1/2) is defined, as i. :)


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endless

Fri Apr 17, 2009 4:39 pm


RE:What does this equal to?

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http://www.google.ca/search?hl=en&safe=off&q=%28-1%29%5E%282%2F3%29&btnG=Search&meta=


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SJ

Fri Apr 17, 2009 6:03 pm


RE:What does this equal to?

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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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saltpro15

Fri Apr 17, 2009 6:13 pm


RE:What does this equal to?

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well, we can't argue with our Google overlords, that must be the correct solution!


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Brightguy

Fri Apr 17, 2009 6:38 pm


Re: What does this equal to?

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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 [url=http://compsci.ca/v3/viewtopic.php?t=15472#141060]two years ago [my post is basically unreadable since LaTeX broke ].


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zero-impact

Fri Apr 17, 2009 6:42 pm


RE:What does this equal to?

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On a similiar note. Today I was playing with imaginary numbers and came up with this
http://www.filedropper.com/second/ea70c9762067dc8270c166bec8081b21.gif
Where did I go horribly wrong??


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apomb

Fri Apr 17, 2009 8:03 pm


Re: RE:What does this equal to?

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On a similiar note. Today I was playing with imaginary numbers and came up with this
http://www.filedropper.com/second/ea70c9762067dc8270c166bec8081b21.gif
Where did I go horribly wrong??

because (-1)(-1) ≠ √1

well... maybe i guess it does


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CodeMonkey2000

Fri Apr 17, 2009 8:35 pm


RE:What does this equal to?

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√1 =+/- 1

There are 2 answers.


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zero-impact

Fri Apr 17, 2009 9:22 pm


RE:What does this equal to?

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does that not still mean that 1 can equal -1 or +1?


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CodeMonkey2000

Fri Apr 17, 2009 9:24 pm


RE:What does this equal to?

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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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zero-impact

Fri Apr 17, 2009 10:04 pm


RE:What does this equal to?

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I understand what you are saying now. I knew it was flawed, I was simply asking how. Thank you.


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Brightguy

Sat Apr 18, 2009 12:23 am


Re: What does this equal to?

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There are 2 answers.
This also came up 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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endless

Sat Apr 18, 2009 7:00 am


Re: What does this equal to?

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There are 2 answers.
This also came up 

ha, reading through that thread is hilarious.