1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex exponential (properties)

  1. May 11, 2005 #1
    Hi, I am solving a second order ODE. the result I got is an exponential to the power of a real and an imaginary part, both of them inside a square root. I need to brake this result into an imaginary and a real part because in this particular case just the imaginary part of the solution is my solution. My question is How can a brake exp (square root of (4+i))?

    thanks

    gomez
     
  2. jcsd
  3. May 11, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Post the ODE.

    Daniel.
     
  4. May 11, 2005 #3
    The ODE is f(r)'' + 1/R* f'(r) - (i+1/r^2)f(r)=0 ; and my boundary conditions are F(r=r1)=1 and F(r=r2) =0. I solved this ODE and I found my two constants but this ODE comes from a PDE which boundary condition is sine(t) whis is the imaginary part of exp(it). my specific question is how can I break and exponential function that comes as a solution of the ODE? I need this solution to have two parts one imaginary and one real, because my solution will be just the imaginary part... is something similar to stoke's problem solution ( fluid mechanics )
     
  5. May 11, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    The equation is quasi linear,i don't think it can be solved that easy.That nonconstant factor spoils everything.I think a numerical solution is the only answer.

    Daniel.
     
  6. May 11, 2005 #5
    Again, my specific question is about the exponential fuction, my solution is exp(root square(4+i)), how can I break this expression into a real part and an imaginary part. is there any property of the exponential function with complex numers that I'm missing?.

    thanks

    pd: the number 4 in my solution just indicates any real number.
     
  7. May 11, 2005 #6

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    [tex] (4+i)^{1/2}=...? [/tex]

    [tex] 4+i=\sqrt{17}\left(\cos\arctan \frac{1}{4}+i\sin\arctan \frac{1}{4}\right) [/tex] (1)

    Then

    [tex] (4+i)^{1/2}=17^{1/4}\left(\cos\frac{\arctan\frac{1}{4}}{2}+i\sin\frac{\arctan\frac{1}{4}}{2}\right) [/tex] (2)

    Simple stuff.

    Daniel.

    P.S.(as an edit) I hope u know how to exponentiate that animal (#2),don't u?
     
    Last edited: May 11, 2005
  8. May 11, 2005 #7
    thanx man, you are really good at this.

    P.S: I don't really have to take the exponential of that, I will just take the imaginary part and represent it as my solution, exp(imaginary).

    P.S.2: people in my lab are still laughing about your "simple stuff" comment

    thanks again
     
  9. May 11, 2005 #8

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    I dunno what u have to do,i said it's weird that u asked for such a simple thing,when the ODE u posted looks awfully difficult.

    Daniel.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Complex exponential (properties)
  1. Exponential integral (Replies: 6)

  2. Laplacian property (Replies: 0)

Loading...