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Define $f:\mathbb{\mathbb{C}}^{2}\rightarrow\mathbb{R}$ by

$$f(z_{1},z_{2})=\text{Arg}(z_{1})+\text{Arg}(z_{2})-\text{Arg}(z_{1}z_{2})\;,$$

where $\text{Arg}$ denotes the principal argument. What is the range of the function $f$? (The answer is $\{-2\pi,0,2\pi\}$.)

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    Where are you stuck?2011-05-30
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    @amWhy: I undid your edit, since Arg was correct, both in being in roman font and in being uppercase -- at least according to http://en.wikipedia.org/wiki/Argument_(complex_analysis).2011-05-30
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    @joriki, no problem, sorry for that!2011-05-30

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