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Math Help - help with this map

  1. #1
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    help with this map

    Show that the mapping w = sin z maps the y-axis one-to-one and onto the v-axis.
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  2. #2
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    Quote Originally Posted by splash View Post
    Show that the mapping w = sin z maps the y-axis one-to-one and onto the v-axis.
    I think you want to show it maps the y-axis one-to-one and onto the x-axis.

    The y-axis are the imaginary numbers xi.

    But that is not true,
    \sin (xi)=xi+\frac{x^3i}{3!}+\frac{x^5i}{5!}+\frac{x^7i  }{7!}+...=i\sinh x
    It still remains an imaginary number. So you established no map.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    I think you want to show it maps the y-axis one-to-one and onto the x-axis.

    The y-axis are the imaginary numbers xi.

    But that is not true,
    \sin (xi)=xi+\frac{x^3i}{3!}+\frac{x^5i}{5!}+\frac{x^7i  }{7!}+...=i\sinh x
    It still remains an imaginary number. So you established no map.
    Where w=u+\bold{i}v, and z=x+\bold{i}y,
    so now it does.

    RonL
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