Taking imaginary integral and derivative

[chaotic]

Homework Statement

when I am solving quantum problem, i see an equation like e^(-kx) e^(icx) i is imaginary. how can i take the integral and derivative of this function

Homework Equations

e^ix ) cosx + isinx

The Attempt at a Solution

actually i tried e^x(-k+ic) and i said the derivative is just (-k+ic)* e^x(-k+ic) :)

please help and teach me!

 

[voko]

What you did is correct. You can treat complex constants as if they were real in differentiation and integration. However, I would recommend getting some introductory text on complex analysis and study it at least until differentiation and integration are introduced.

 

[chaotic]

when i take the same derivative with wolfram i get another result http://www.wolframalpha.com/input/?i=d(e^(-kx)+e^(icx))/dx

 

[voko]

That's because it is confused by the input. Note it treats "icx" as all caps CIX and assumes it is a constant.

 

[chaotic]

agh :) thank you very much i understand now :)

 

[haruspex]

when i take the same derivative with wolfram i get another result http://www.wolframalpha.com/input/?i=d(e^(-kx)+e^(icx))/dx

Wolfram seems to have treated the second x as some constant X. In fact, it looks suspiciously as though it has interpreted "icx" as Roman Numerals "CIX" (109). Bizarre.

 

[chaotic]

yes it is very confusing I am trying to find solution for 2 hours just because of that it is funny it takes my precious time :)

 

[voko]

A space after i and before c does wonders. But the output is still a bit odd.

 

[SammyS]

A space after i and before c does wonders. But the output is still a bit odd.

Yes, $\ \ i(c+i k) e^{-k x+i c x}\ \$ is a bit odd, isn't it?