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arindameducationusc

  • one year ago

Can anyone explain x^pi?

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  1. ParthKohli
    • one year ago
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    It's \(x\) raised to the power \(\pi\).

  2. arindameducationusc
    • one year ago
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    yes, i will upload the graph... I have a doubt. wait..

  3. arindameducationusc
    • one year ago
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    Ya this one

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  4. arindameducationusc
    • one year ago
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    The imaginary part and real part...

  5. arindameducationusc
    • one year ago
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    Can you explain...

  6. ParthKohli
    • one year ago
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    For a positive number, this is of course a purely real number. Thus the imaginary part is zero.

  7. ParthKohli
    • one year ago
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    You do understand complex numbers, right?

  8. arindameducationusc
    • one year ago
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    Yes I understand Complex numbers. So that means we can graph complex numbers? I didn't know that!

  9. ParthKohli
    • one year ago
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    Yeah. For negative \(x\), this function has complex values.

  10. arindameducationusc
    • one year ago
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    Do you have any reference in which I can study complex number graphs, any good books or video link?

  11. Astrophysics
    • one year ago
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    http://www.mathsisfun.com/numbers/complex-numbers.html

  12. Astrophysics
    • one year ago
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    khanacademy is awesome for all math

  13. Astrophysics
    • one year ago
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    as well

  14. arindameducationusc
    • one year ago
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    Then if x=3, then 3^3.14 should be real, but in graph it is imaginary..

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  15. anonymous
    • one year ago
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    Its just x^3.14

  16. zepdrix
    • one year ago
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    @arindameducationusc You'll notice that the orange line stays on the x-axis when x is positive. The imaginary part is zero for all positive x. So there is no imaginary part over there.

  17. arindameducationusc
    • one year ago
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    I got it...@zepdrix @jcoury @Astrophysics @ParthKohli Thank you to all for helping.....

  18. phi
    • one year ago
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    you may know \[ e^{i\pi}= \cos\pi + i \sin \pi = -1 + 0 \ i = -1 \] when x is negative, x^pi is the same as \[ (- |x|)^\pi = \left( e^{i\pi} |x|\right)^\pi \\= e^{i\pi^2} |x|^\pi= (\cos\pi^2 + i \sin \pi^2)|x|^\pi \\ (-x)^\pi \cos\pi^2 + i (-x)^\pi \sin \pi^2 \] which has a non-zero imaginary component

  19. Astrophysics
    • one year ago
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    ^ Yes, that's very useful, Euler's equation

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