I see this all the time in Mathematica output as well as in text, such as near the top of the Wikipedia Beta function page.
What does $\mathrm{Re}(x)$ mean?
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$\begingroup$
notation
complex-numbers
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4As$a$tiny *Mathematica* tip: whenever you see some function you don't quite understand in the output, highlight the name of the function (by double-clicking, for instance) and press the `F1` key. – 2011-10-06
2 Answers
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The real part of the complex number x. If you haven't seen complex numbers before, they're a two-dimensional version of the normal real numbers.
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1@Tyler: $\mathrm{Im}(z)$ is certainly real; what you probably had in mind is that if one considers the Argand plane, $\mathrm{Im}(z)$ is equivalent to the vertical coordinate of the point $z$. – 2011-10-06
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If a complex number $z$ is written as $z = a + bi$, then Re$(z) = a$ and Im$(z) = b$. (At risk of stating the obvious, "Re" stands for "Real" and "Im" stands for "Imaginary".)
If we visualize complex numbers as vectors in $\mathbb{R}^2$, Re is the projection onto the real axis, and Im is onto the imaginary axis. So $z = \mathrm{Re}(z) + \mathrm{Im}(z)i$.
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0@Tyler: The only **real** numbers on the unit circle of the complex plane are +1, -1, since real numbers are restricted to the real line and there are only these two points of intersection. There are an infinite number of **complex** numbers on the unit circle, of course. – 2011-10-06