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Math Help - Conjugate of the derivative...

  1. #1
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    Conjugate of the derivative...

    Hi everyone,
    I need help with the following:

    If f is C^1 show that

    \left( \frac{\partial}{\partial z} f \right)^* =  \frac{\partial}{\partial z^*} f^*

    where ^ * is the complex conjugate. I am not sure what f^* is so I have no place to start. Any help is greatly appreciated. Thanks
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  2. #2
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    If ^* is the complex conjugate, then f^* is the complex conjugate of f..... It may help you to write f(x,y) = u(x,y) + i v(x,y) and then use the facts that x=\frac{z+z^*}2 and y=\frac{z-z^*}2.
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  3. #3
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    Quote Originally Posted by maddas View Post
    If ^* is the complex conjugate, then f^* is the complex conjugate of f..... It may help you to write f(x,y) = u(x,y) + i v(x,y) and then use the facts that x=\frac{z+z^*}2 and y=\frac{z-z^*}2.
    Can I always write f in such a form? That was my problem. I will try what you said in the meantime, thanks.
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  4. #4
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    Yes, you may. Btw, your name is cool.
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  5. #5
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    Quote Originally Posted by maddas View Post
    Yes, you may. Btw, your name is cool.
    Pretty cool eh
    Thanks again
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