Results 1 to 6 of 6

Math Help - complex analytic functions

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    43

    complex analytic functions

    hi to all can i please see the answer for this to check what i have been doing wrong thanks heaps.
    (a) Where is the function
    f(z) = z/(1+iz)^4 analytic?

    (b) Find
    f(-i).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member vincisonfire's Avatar
    Joined
    Oct 2008
    From
    Sainte-Flavie
    Posts
    469
    Thanks
    2
    Awards
    1
    a) Plug f(z) in the Cauchy-Riemann equations and see where they are satisfied
    b) Replace z by -i
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by sandy View Post
    hi to all can i please see the answer for this to check what i have been doing wrong thanks heaps.
    (a) Where is the function
    f(z) = z/(1+iz)^4 analytic?

    (b) Find
    f(-i).
    Quote Originally Posted by vincisonfire View Post
    a) Plug f(z) in the Cauchy-Riemann equations and see where they are satisfied
    b) Replace z by -i
    What vincisonfire said is true, but surely you have proved that any rational function in \mathbb{C} is analytic everywhere it's denominator is non-zero, right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2010
    Posts
    43
    Quote Originally Posted by vincisonfire View Post
    a) Plug f(z) in the Cauchy-Riemann equations and see where they are satisfied
    b) Replace z by -i
    can i please have a hint of how to break it up
    do i substitute z by x+iy but then its to big
    what do i do?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member vincisonfire's Avatar
    Joined
    Oct 2008
    From
    Sainte-Flavie
    Posts
    469
    Thanks
    2
    Awards
    1
    It is a bit messy.
    It may be simpler in this form :
     f(z)  = \frac{z}{(1+iz)^4} =  \frac{r_1e^{i\theta_1}}{(r_2e^{i\theta_2})^{4}} =  \frac{r_1e^{i\theta_1}}{r_2^4e^{4i\theta_2}}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Apr 2010
    Posts
    43
    Quote Originally Posted by vincisonfire View Post
    It is a bit messy.
    It may be simpler in this form :
     f(z) = \frac{z}{(1+iz)^4} = \frac{r_1e^{i\theta_1}}{(r_2e^{i\theta_2})^{4}} = \frac{r_1e^{i\theta_1}}{r_2^4e^{4i\theta_2}}
    thanks so much for your help i done it and found that cauchy riemann equations are satisfied every where so do we say f(z) is analytic everywhere on C??
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex Analysis-Analytic Functions
    Posted in the Advanced Math Topics Forum
    Replies: 7
    Last Post: June 19th 2010, 12:39 PM
  2. complex analysis analytic functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 16th 2010, 07:49 PM
  3. Complex analytic functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 25th 2010, 05:49 AM
  4. complex analytic functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 6th 2008, 07:45 PM
  5. analytic complex functions
    Posted in the Calculus Forum
    Replies: 8
    Last Post: May 15th 2007, 08:55 PM

Search Tags


/mathhelpforum @mathhelpforum