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Math Help - [SOLVED] Complex

  1. #1
    Member ronaldo_07's Avatar
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    [SOLVED] Complex

    Which of the following functions are entire? Give reasons.

    (i) f(z) = sin |z|,

    (ii) f(z) = z^5 + iz^7 + z^{12},

    (iii) f(z) = f(x + iy) = x,

    (iv) f(z) = 2.
    Last edited by ronaldo_07; February 4th 2009 at 10:56 AM.
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  2. #2
    Member ronaldo_07's Avatar
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    How would I know if the function is entire?
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  3. #3
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    Quote Originally Posted by ronaldo_07 View Post
    How would I know if the function is entire?
    You would test it by applying the definition .....
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    Member ronaldo_07's Avatar
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    what definition would I use I have no clue.
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    Quote Originally Posted by ronaldo_07 View Post
    what definition would I use I have no clue.
    Entire function - Wikipedia, the free encyclopedia
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    Quote Originally Posted by ronaldo_07 View Post
    (i) f(z) = sin |z|
    This function is bounded, so if it was entire then it would be a constant.
    This is a contradiction so it is not entire.

    (ii) f(z) = z^5 + iz^7 + z^{12},
    Polynomials are always entire.

    (iii) f(z) = f(x + iy) = x
    Check the Cauchy-Riemann equations

    (iv) f(z) = 2.
    Polynomials are always entire.
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