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Math Help - Complex analysis, need bright light

  1. #1
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    Question Complex analysis, need bright light

    Hello,

    I'm not a mathematician but I'm trying to help a friend here struggled with this , this is naturally why I went to this forum:

    If C is the semicircle \left| z \right| =2,Re(z)>0,prove that

    Hopping that a good soul could help me.
    Last edited by Izanagi; December 8th 2009 at 04:40 PM.
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  2. #2
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    Quote Originally Posted by Izanagi View Post
    Hello,

    I'm not a mathematician but I'm trying to help a friend here struggled with this , this is naturally why I went to this forum:

    If C is the semicircle ,,prove that

    Hopping that a good soul could help me.
    What is the integration with respect to?? Be that as it may, start by noting that a general property of integrals is \left| \int ( ) \right| \leq \int |( ) |.
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  3. #3
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    Thank you for your reply,

    I've made mistake in the formula, I just edit it.

    and i understand \left| \int ( ) \right| \leq \int |( ) | but later what should we do for x^4+iy^4 ?

    Would you have hint to solve this?

    thanks again
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  4. #4
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    Quote Originally Posted by Izanagi View Post
    Thank you for your reply,

    I've made mistake in the formula, I just edit it.

    and i understand \left| \int ( ) \right| \leq \int |( ) | but later what should we do for x^4+iy^4 ?

    Would you have hint to solve this?

    thanks again
    On C, |dz| = 4 \pi and |x^4 + i y^4| = 8 |\cos^4 \theta + i \sin^4 \theta| \leq 8 |\cos \theta + i \sin \theta| = 8.
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  5. #5
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    Hello,

    Thanks a lot for your help, that is brilliant. With your explanations my friend has been able to solve this.
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