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Math Help - Complex transformation query

  1. #1
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    Complex transformation query

    Let the region R be defined by |z|<1, if z is any point in the region R, and z^* is its conjugate, find the corresponding region for w where

    w=zz^*

    My solution was this. I know that zz^*=|z|^2 and since the modulus of a complex number is a real number its square will be also. So we know w is a real number and so will lie on the real line. In addition its modulus will be less than one, so I think w lies on the real axis between 0 and 1.

    However the book says that it's any point inside the unit circle centered at the origin (i.e. no change). But wouldn't this be true for |w|=zz^*?? The book definitely asks for w=zz^*, so is there a typo on the book or have I made a mistake?

    Regards,

    Stonehambey
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  2. #2
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    Quote Originally Posted by Stonehambey View Post
    Let the region R be defined by |z|<1, if z is any point in the region R, and z^* is its conjugate, find the corresponding region for w where w=zz^*

    However the book says that it's any point inside the unit circle centered at the origin (i.e. no change). But wouldn't this be true for |w|=zz^*?? The book definitely asks for w=zz^*, so is there a typo on the book or have I made a mistake?
    I agree with you. The way the problem defines w, we get w\in \Re~\&~0\le w<0.
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