Question

Can someone explain to me complex exponents? Like, infinity Thanks
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x^-sqrt(-pi)

Answer 1

@derk765 @jim_thompson5910

Answer 2

Well at first you can simplify this, using the following rule,
\[b^{-a}=\frac{1}{b^{a}}\]

Answer 3

OH wait oops, I meant infinity times the denominator I had, so ignore the negative on the square root oops sorry

Answer 4

Sp what is it then, please rewrite it.

Answer 5

\[\frac{ \infty }{ x ^{\sqrt{-\pi}} }\]

Answer 6

I don't know, sorry.

Answer 7

I know right!? It's so confusing, complex numbers are complex (da dun chsh) to begin with but to have a HYPER COMPLEX NUMBER WITH A COMPLEX EXPONENT?! D:

Answer 8

You don't even cover complex and hyper complex numbers in linear algebra or partial differential equations, which are pretty high level mathematics

Answer 9

The presence of infinity in this expression hopefully will get sorted out as you analyze it, as for the complex exponent:

complex exponents can be examined using the cis function:
e^(ix) = cosx + i sin(x)

In this case, x^sqrt(-pi) = e^ln(x^sqrt(-pi)) = e^(i * sqrt(pi) * ln(x))

so it could be analyzed this way: cos(sqrt(pi) * ln(x)) + i sin(sqrt(pi) * ln(x))

All the solutions to the cis function exist on the unit circle in the complex plane, so there are a limited number of values which you are dividing infinity by. All of these values are finite and, with the exception of 1 and -1, complex. So the answer would be some form of infinity is my initial take.

Answer 10

THANK YOU I never actually thought someone would answer it with an intelligent answer xD
Thanks! *cough* fan *cough* :)