The conjugate(x) function computes the complex conjugate of x.

You can enter the command conjugate using either the 1-D or 2-D calling sequence. For example, conjugate(3 + 5*I) is equivalent to $\stackrel{\&conjugate0;}{\left(3+5\mathrm{I}\right)}$.

If x includes a function f, then conjugate(x) executes the procedure `conjugate/f` (if it exists) to compute the conjugate of the corresponding part of the expression.

By this method, the functionality of this command can be extended.  For example, recording that a function f is conjugate symmetric can be accomplished by defining the following function.

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

The conjugate command is thread-safe as of Maple 15.

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

$\mathrm{conjugate}\left(3+5\mathrm{I}\right)$

$3-5\mathrm{I}$

$\mathrm{conjugate}\left(\left(3+5\mathrm{I}\right)z\right)$

$\left(3-5\mathrm{I}\right)\stackrel{\&conjugate0;}{z}$

$\mathrm{conjugate}\left(3-\mathrm{I}\right)$

$3+\mathrm{I}$

$\mathrm{conjugate}\left(5\mathrm{I}\right)$

$-5\mathrm{I}$

$\mathrm{conjugate}\left(x^2-y\right)$

$\stackrel{\&conjugate0;}{\left(x^2-y\right)}$

$\mathrm{conjugate}\left(\mathrm{sqrt}\left(-1\right)\right)$

$\mathrm{-I}$

$\mathrm{conjugate}\left(\sin \left(\exp \left(1\right)\right)\right)$

$\sin \left(\ⅇ\right)$

$\mathrm{conjugate}\left(\exp \left(3\mathrm{I}\right)\right)$

$\frac{1}{{\ⅇ}^{3\mathrm{I}}}$

$\mathrm{conjugate}\left(\exp \left(1-\mathrm{I}\right)\right)$

${\ⅇ}^{1+\mathrm{I}}$

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

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

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

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

The conjugate command was updated in Maple 2016; see Advanced Math.