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