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I need to prove that $z=x+iy$ equals infinity is equivalent to $x = \infty$ and $y=\infty$.

I also have to give an example of a complex number $z$ so that $\sin(z)=\infty$.

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    Your first question amounts to showing the false if and only if false and false (which is easy). In other words, a complex number is _never_ infinity, nor are $x$ and $y$ in a valid expression $x+iy$ ever infinity. And your second question therefore has no good answer. \n\n Infinity only arises in taking limits of _expressions_, and so you should probably restate your question in those terms (however I don't think that statement is actually true in the usual sense of complex and real infinity, occuring as limits).2012-05-19

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