Results 1 to 5 of 5

Math Help - Another HARD complex question

  1. #1
    Newbie
    Joined
    May 2006
    Posts
    3

    Another HARD complex question

    Need to do these by tomorrow morning. Any last minute help welcome. Cheers

    Which of the following functions are holomorphic at z=0? Prove your answer
    A) lzlsquared
    B)Re(z) + Im(z)
    C)Re(z).Im(z)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by sg2004 View Post
    Need to do these by tomorrow morning. Any last minute help welcome. Cheers

    Which of the following functions are holomorphic at z=0? Prove your answer
    A) lzlsquared
    B)Re(z) + Im(z)
    C)Re(z).Im(z)
    (C) has been done in this recent thread, it is equivalent to problem (b) there.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by sg2004 View Post
    B)Re(z) + Im(z)
    f(x+i y) = x+y

    does not satisfy the Cauchy-Riemann equations at z=0.

    (du/dx=1, but dv/dy=0)

    RonL
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by sg2004 View Post
    A) lzlsquared
    Is not holomorphic at z=0, as though it satisfies the Cauchy-Riemann
    equations there, it does not satisfy them at any other point, so it is
    not complex differentiable in any neighbourhood of 0.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2006
    Posts
    3
    Thanks so much Capn Black.... Cheers!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex Variable Hard Question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 7th 2011, 08:44 AM
  2. Hard complex analysis question help Please!
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: April 17th 2009, 06:14 AM
  3. another hard complex analysis question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 12th 2009, 04:59 AM
  4. complex no's<<<hard!
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 3rd 2008, 12:54 PM
  5. hard complex question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 22nd 2006, 11:34 AM

Search Tags


/mathhelpforum @mathhelpforum