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How do I prove that $$\lim_{z\to0}\frac{\Re(z)\Im(z)}{|z|}=0? $$ I've tried it using $\varepsilon-\delta$ language, but can't really get anywhere.

Any hints would be greatly appreciated.

Thanks.

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    The same limit came up in another question: http://math.stackexchange.com/questions/26672/finding-limit-of-function-with-more-than-one-variable2011-04-16

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