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Plasmataco

  • one year ago

what is the sqrt of i(imaginary)

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  1. Plasmataco
    • one year ago
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    \[\sqrt[4]{-1}\]

  2. Plasmataco
    • one year ago
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    ppl... @jim_thompson5910 @dan815

  3. Plasmataco
    • one year ago
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    @dan815 ? ur like the smartest guy ever so...

  4. Plasmataco
    • one year ago
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    tied for @jim_thompson5910

  5. Plasmataco
    • one year ago
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    haaaaalp

  6. jim_thompson5910
    • one year ago
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    so you're asking why this is true? \[\Large \sqrt{i} = \sqrt[4]{-1}\]

  7. Plasmataco
    • one year ago
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    no, what does it equal.

  8. Plasmataco
    • one year ago
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    is there like a different letter for that?

  9. jim_thompson5910
    • one year ago
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    I just said it \(\LARGE \sqrt{i}\) is equal to \(\LARGE \sqrt[4]{-1}\)

  10. Plasmataco
    • one year ago
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    but to reduce it without a radical sign.

  11. jim_thompson5910
    • one year ago
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    \[\Large \sqrt{i} = \sqrt{\sqrt{-1}}\] \[\Large \sqrt{i} = \sqrt{(-1)^{1/2}}\] \[\Large \sqrt{i} = ((-1)^{1/2})^{1/2}\] \[\Large \sqrt{i} = (-1)^{1/2*1/2}\] \[\Large \sqrt{i} = (-1)^{1/4}\] \[\Large \sqrt{i} = \sqrt[4]{-1}\]

  12. Plasmataco
    • one year ago
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    Im sry i might be asking the impossible.

  13. jim_thompson5910
    • one year ago
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    You can either write it with a fractional exponent, or as a radical. I don't think it's possible to do it any other way

  14. Plasmataco
    • one year ago
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    nvm

  15. Plasmataco
    • one year ago
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    gtg tho bye

  16. anonymous
    • one year ago
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    The answer to your question is \[\frac{1+i}{\sqrt 2}\]

  17. Plasmataco
    • one year ago
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    oh. sry afk but thx!

  18. IrishBoy123
    • one year ago
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    \(\large \sqrt{i}=\frac{1+i}{\sqrt{2}}\) but why not also \(\large -\frac{1+i}{\sqrt{2}}\)?? \(\large\sqrt{e^{i \frac{\pi}{2} + 2n \pi}} = e^{i \frac{\pi}{4} + n \pi} = e^{i \frac{\pi}{4}}, e^{i \frac{5\pi}{4}}\) |dw:1442740104302:dw|

  19. anonymous
    • one year ago
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    That's also true, of course. I was answering the question in the same way that one might say "The square root of nine is three". If we're being strict about it, the radical sign should not be used in this context because it only applies to positive, real numbers. It should be written something like \[ i^{1/2} =\left\{ \frac{(1+i)}{\sqrt{2}} , -\frac{1+i}{\sqrt{2}} \right\}\] \(\sqrt{i},\sqrt{-1}\), and other things like that don't actually make sense.

  20. IrishBoy123
    • one year ago
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    thank you

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