Show that the mapping w = sin z maps the y-axis one-to-one and onto the v-axis.

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- Nov 16th 2006, 04:21 AM #1

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- Nov 16th 2006, 06:18 AM #2

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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 $\displaystyle xi$.

But that is not true,

$\displaystyle \sin (xi)=xi+\frac{x^3i}{3!}+\frac{x^5i}{5!}+\frac{x^7i }{7!}+...=i\sinh x$

It still remains an imaginary number. So you established no map.

- Nov 16th 2006, 07:54 AM #3

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