Let [itex]f(z)=z+\frac{1}{z}[/itex], the question is to find the image of this function on [itex]|z|>1[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

To do so, I tried to find the image of the unit circle which is the interval [-2,2] and so I could not determine our image.

If also we tried to find the image of f we get

[itex]f(re^{i\theta})=u+iv[/itex]

where

[itex]u(re^{i\theta})=(r+\frac{1}{r})\cos \theta[/itex]

and

[itex]v(re^{i\theta})=(r-\frac{1}{r})\sin \theta[/itex]

with r>1.

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# Image of a complex function

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