conjugate - Maple Help

conjugate

return the complex conjugate

Calling Sequence

 conjugate(x) $\stackrel{&conjugate0;}{x}$

Parameters

 x - expression

Description

 • 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 $\stackrel{&conjugate0;}{\left(3+5I\right)}$.
 • 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.

conjugate/f := proc(x) f(conjugate(x)) end proc;

 • 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.

Examples

 > $\mathrm{conjugate}\left(3+5I\right)$
 ${3}{-}{5}{}{I}$ (1)
 > $\mathrm{conjugate}\left(\left(3+5I\right)z\right)$
 $\left({3}{-}{5}{}{I}\right){}\stackrel{{&conjugate0;}}{{z}}$ (2)
 > $\mathrm{conjugate}\left(3-I\right)$
 ${3}{+}{I}$ (3)
 > $\mathrm{conjugate}\left(5I\right)$
 ${-}{5}{}{I}$ (4)
 > $\mathrm{conjugate}\left({x}^{2}-y\right)$
 $\stackrel{{&conjugate0;}}{\left({{x}}^{{2}}{-}{y}\right)}$ (5)
 > $\mathrm{conjugate}\left(\mathrm{sqrt}\left(-1\right)\right)$
 ${-I}$ (6)
 > $\mathrm{conjugate}\left(\mathrm{sin}\left(\mathrm{exp}\left(1\right)\right)\right)$
 ${\mathrm{sin}}{}\left({ⅇ}\right)$ (7)
 > $\mathrm{conjugate}\left(\mathrm{exp}\left(3I\right)\right)$
 $\frac{{1}}{{{ⅇ}}^{{3}{}{I}}}$ (8)
 > $\mathrm{conjugate}\left(\mathrm{exp}\left(1-I\right)\right)$
 ${{ⅇ}}^{{1}{+}{I}}$ (9)
 > $\mathrm{conjugate}\left(\mathrm{ln}\left(-1\right)\right)$
 ${-I}{}{\mathrm{\pi }}$ (10)
 > $\mathrm{conjugate}\left(\mathrm{polar}\left(3,\frac{\mathrm{\pi }}{7}\right)\right)$
 ${\mathrm{polar}}{}\left({3}{,}{-}\frac{{\mathrm{\pi }}}{{7}}\right)$ (11)

Compatibility

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