Results 1 to 3 of 3

Thread: real part of a function

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    7

    real part of a function

    hi, this is a stupid question but is the real part of the function

    $\displaystyle f(z) = e^{iz} $


    $\displaystyle cos z $ ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by Adre5 View Post
    hi, this is a stupid question but is the real part of the function

    $\displaystyle f(z) = e^{iz} $


    $\displaystyle cos z $ ?
    No, it's not.

    Remember that $\displaystyle z$ is a complex number.

    In other words, $\displaystyle z = x + iy$.


    You need to write $\displaystyle f(z) = e^{iz}$ as $\displaystyle u + iv$, where $\displaystyle u, v$ are real functions of $\displaystyle x$ and $\displaystyle y$.


    So $\displaystyle f(z) = e^{iz}$

    $\displaystyle = e^{i(x + iy)}$

    $\displaystyle = e^{ix + i^2y}$

    $\displaystyle = e^{-y + ix}$

    $\displaystyle = e^{-y}e^{ix}$

    $\displaystyle = e^{-y}(\cos{x} + i\sin{x})$ by Euler's Rule

    $\displaystyle = e^{-y}\cos{x} + i\,e^{-y}\sin{x}$.

    $\displaystyle = u + iv$.


    So the real part of $\displaystyle e^{iz}$ is $\displaystyle e^{-y}\cos{x}$ and the imaginary part of $\displaystyle e^{iz}$ is $\displaystyle e^{-y}\sin{x}$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    7
    ohh thank you!! you made it so clear for me
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find an analytic function from its real part
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Sep 23rd 2011, 04:17 PM
  2. Replies: 1
    Last Post: Feb 3rd 2010, 01:44 PM
  3. Fixed Real Numbers...Part 3
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Dec 8th 2009, 07:02 AM
  4. Fixed Real Numbers...Part 2
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Dec 8th 2009, 07:00 AM
  5. imagine and real part of inner product?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Nov 9th 2009, 07:24 AM

Search Tags


/mathhelpforum @mathhelpforum