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arindameducationusc
 one year ago
Can anyone explain x^pi?
arindameducationusc
 one year ago
Can anyone explain x^pi?

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ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1It's \(x\) raised to the power \(\pi\).

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0yes, i will upload the graph... I have a doubt. wait..

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0Ya this one

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0The imaginary part and real part...

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0Can you explain...

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1For a positive number, this is of course a purely real number. Thus the imaginary part is zero.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1You do understand complex numbers, right?

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0Yes I understand Complex numbers. So that means we can graph complex numbers? I didn't know that!

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1Yeah. For negative \(x\), this function has complex values.

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0Do you have any reference in which I can study complex number graphs, any good books or video link?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1khanacademy is awesome for all math

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0Then if x=3, then 3^3.14 should be real, but in graph it is imaginary..

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0@arindameducationusc You'll notice that the orange line stays on the xaxis when x is positive. The imaginary part is zero for all positive x. So there is no imaginary part over there.

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0I got it...@zepdrix @jcoury @Astrophysics @ParthKohli Thank you to all for helping.....

phi
 one year ago
Best ResponseYou've already chosen the best response.0you 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 nonzero imaginary component

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1^ Yes, that's very useful, Euler's equation
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