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

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.

$\mathrm{simplify}\left({\mathrm{polar}\left(a\,b\right)}^2\mathrm{polar}\left(c\,d\right)\,\mathrm{polar}\right)$

$\mathrm{polar}\left(a^{2}c\,2b+d\right)$

$\mathrm{simplify}\left(2\mathrm{polar}\left(a\,c\right)\+\mathrm{polar}\left(b\,c\right)\+\mathrm{polar}\left(d\,-c\right)\,\mathrm{polar}\right)$

$\mathrm{polar}\left(2a+b-d\,c\right)$

$\mathrm{simplify}\left(\mathrm{polar}\left(1\,0\right)\+\mathrm{polar}\left(1\,\mathrm{evalf}\left(\frac{\mathrm{Pi}}{2}\right)\right)\,\mathrm{polar}\right)$

$\mathrm{polar}\left(1.414213562\,0.7853981635\right)$