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Let $t \in \mathbb{C}$ and consider the map $k(t)= \frac{1}{t+i}$

What happens to all horizontal/vertical lines under the map $k$? Describe geometrically.

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What have you tried? Where did you get stuck? This looks like you've just copied a problem from a textbook and that is not the best way to get really good help here. –  mrf Mar 6 '13 at 22:52
if this is a homework problem, please add the homework tag. –  gt6989b Mar 6 '13 at 22:53
I'm sure you can answer the question about the domain of $k$. I can't imagine someone would get to a complex analysis course without having worked with the notion of the domain of a function in some previous course. Show us what you can do, we'll help you with the rest. –  Gerry Myerson Mar 6 '13 at 23:11

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