simplify complex-valued expressions involving polar forms - Maple Help

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simplify/polar - simplify complex-valued expressions involving polar forms

 Calling Sequence simplify(expr, polar)

Parameters

 expr - any expression polar - literal name; polar

Description

 • The simplify/polar function is used to simplify complex-valued expressions by applying the identities

${\mathrm{polar}\left(a,b\right)}^{r}\to \mathrm{polar}\left({a}^{r},rb\right)\mathrm{if}r\mathrm{is}\mathrm{real}$

$r\mathrm{polar}\left(a,b\right)\to \mathrm{polar}\left(ra,b\right)\mathrm{if}r\mathrm{is}\mathrm{real}$

$\mathrm{polar}\left(a,b\right)\mathrm{polar}\left(c,d\right)\to \mathrm{polar}\left(ac,b+d\right)$

$\mathrm{polar}\left(a,c\right)+\mathrm{polar}\left(b,±c\right)\to \mathrm{polar}\left(a±b,c\right)$

 Furthermore, a sum of polars with numeric arguments is combined if at least one term has floating-point arguments.  For more general sums of polars, use evalc.

Examples

 > $\mathrm{simplify}\left({\mathrm{polar}\left(a,b\right)}^{2}\mathrm{polar}\left(c,d\right),\mathrm{polar}\right)$
 ${\mathrm{polar}}{}\left({{a}}^{{2}}{}{c}{,}{2}{}{b}{+}{d}\right)$ (1)
 > $\mathrm{simplify}\left(2\mathrm{polar}\left(a,c\right)+\mathrm{polar}\left(b,c\right)+\mathrm{polar}\left(d,-c\right),\mathrm{polar}\right)$
 ${\mathrm{polar}}{}\left({2}{}{a}{+}{b}{-}{d}{,}{c}\right)$ (2)
 > $\mathrm{simplify}\left(\mathrm{polar}\left(1,0\right)+\mathrm{polar}\left(1,\mathrm{evalf}\left(\frac{\mathrm{π}}{2}\right)\right),\mathrm{polar}\right)$
 ${\mathrm{polar}}{}\left({1.414213562}{,}{0.7853981635}\right)$ (3)