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combine/conjugate

combine complex conjugates

 Calling Sequence combine(x, conjugate)

Parameters

 x - any expression

Description

 • Expressions involving conjugates are combined by applying the following transformations:

$\mathrm{conjugate}\left(a\right)+\mathrm{conjugate}\left(b\right)\to \mathrm{conjugate}\left(a+b\right)$

$\mathrm{conjugate}\left(a\right)\mathrm{conjugate}\left(b\right)\to \mathrm{conjugate}\left(ab\right)$

${\mathrm{conjugate}\left(a\right)}^{r}\to \mathrm{conjugate}\left({a}^{r}\right)\mathrm{if}r\mathrm{is}\mathrm{real}$

 • In 2-D Math, the conjugate of an expression is depicted by a horizontal bar above the expression.

Examples

 > $\mathrm{combine}\left(\mathrm{conjugate}\left(x\right)+\mathrm{conjugate}\left(y\right),\mathrm{conjugate}\right)$
 $\stackrel{{&conjugate0;}}{\left({x}{+}{y}\right)}$ (1)
 > $\mathrm{combine}\left(\mathrm{conjugate}\left(x\right)+{\mathrm{conjugate}\left(x\right)}^{2}+\mathrm{conjugate}\left({x}^{3}\right),\mathrm{conjugate}\right)$
 $\stackrel{{&conjugate0;}}{\left({{x}}^{{3}}{+}{{x}}^{{2}}{+}{x}\right)}$ (2)
 > $\mathrm{combine}\left({\mathrm{conjugate}\left(x\right)}^{3}+3\mathrm{conjugate}\left(y\right)\mathrm{conjugate}\left(z\right),\mathrm{conjugate}\right)$
 ${\stackrel{{&conjugate0;}}{{x}}}^{{3}}{+}{3}{}\stackrel{{&conjugate0;}}{\left({y}{}{z}\right)}$ (3)
 > $\mathrm{combine}\left({\mathrm{conjugate}\left(x\right)}^{3}+\mathrm{conjugate}\left(y\right)\mathrm{conjugate}\left(z\right),\mathrm{conjugate}\right)$
 $\stackrel{{&conjugate0;}}{\left({{x}}^{{3}}{+}{y}{}{z}\right)}$ (4)