What does $\mathrm{Re}(x)$ mean?

$\begingroup$

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.

$\endgroup$ 3

2 Answers

$\begingroup$

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 $z = \mathrm{Re}(z) + \mathrm{Im}(z)i$.

$\endgroup$ 3 $\begingroup$

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.

$\endgroup$ 2

You Might Also Like