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The Re(x) calling sequence attempts to return the real part of x.

If x is a real extended numeric, then x is returned. If x is a complex extended numeric, then the real part of x is returned.

The Im(x) function attempts to return the imaginary part of x.

If x is a real extended numeric, then 0 is returned. If x is a complex extended numeric, then the imaginary part of x is returned.

You can enter the commands Re and Im using their 1-D or 2-D calling sequences. For example, Re(3+4*I) is equivalent to $\mathrm{\Re }\left(3+4\mathrm{I}\right)$.

If x includes a function f, then Re(x) and Im(x) attempt to execute the procedures `Re/f` and `Im/f` to determine the real and imaginary parts of the corresponding part of x.

By this method, the functionality of these commands can be extended. For example, Re(sin(3+4*I)*ln(3+4*I)) executes the procedures `Re/sin`, `Im/sin`, `Re/ln`, and `Im/ln`.

To specify that unknown variables should be assumed to represent real values, use the assume or the evalc command.

The Re and Im commands are thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe .

$\mathrm{\Re }\left(x\right)$

$\mathrm{\Re }\left(x\right)$

$\mathrm{\Im }\left(xy\right)$

$\mathrm{\Im }\left(xy\right)$

$\mathrm{assume}\left(z\,\mathrm{real}\right)$

$\mathrm{\Re }\left(xy+z\right)$

$\mathrm{z~}+\mathrm{\Re }\left(xy\right)$

$\mathrm{\Re }\left(xz\right)$

$\mathrm{z~}\mathrm{\Re }\left(x\right)$

$\mathrm{\Re }\left(\mathrm{\pi }+\mathrm{I}\exp \left(1\right)\right)$

$\mathrm{\pi }$

$\mathrm{\Re }\left(\cosh \left(3+4\mathrm{I}\right)\right)$

$\cosh \left(3\right)\cos \left(4\right)$

$\mathrm{\Im }\left(\cosh \left(3+4\mathrm{I}\right)\right)$

$\sinh \left(3\right)\sin \left(4\right)$

$\mathrm{\Im }\left(\exp \left(\mathrm{I}\right)\right)$

$\sin \left(1\right)$

$\ln \left(-1\right)$

$\mathrm{I}\mathrm{\pi }$

$\mathrm{\Im }\left(\ln \left(-1\right)\right)$

$\mathrm{\pi }$

$\mathrm{\Im }\left(\mathrm{polar}\left(3\,\frac{\mathrm{\pi }}{7}\right)\right)$

$3\sin \left(\frac{\mathrm{\pi }}{7}\right)$

$\mathrm{\Re }\left(\mathrm{polar}\left(\exp \left(x+4\mathrm{I}\right)\right)\right)$

${\ⅇ}^{\mathrm{\Re }\left(x\right)}\cos \left(\arg \left({\ⅇ}^{x+4\mathrm{I}}\right)\right)$

$\mathrm{evalc}\left(\right)$

${\ⅇ}^x\cos \left(4\right)$