conjugate - Maple Programming 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 $\stackrel{&conjugate0;}{3+5I}$.
 • 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.

$\mathrm{conjugate/f}≔\mathbf{proc}\left(x\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}f\left(\mathrm{conjugate}\left(x\right)\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{end proc}$

 • 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

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

Compatibility

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