The polar(z) calling sequence converts the complex-valued expression z to its representation in polar coordinates.

The expression is represented as polar(r, t) where r is the modulus and t is the argument of the complex value of the expression.

This function can also be invoked as a convert function: convert(z, polar).  See convert/polar.

$\mathrm{polar}\left(3+4\mathrm{I}\right)$

$\mathrm{polar}\left(5\,\arctan \left(\frac{4}{3}\right)\right)$

$\mathrm{convert}\left(3+4\mathrm{I}\,\mathrm{polar}\right)$

$\mathrm{polar}\left(5\,\arctan \left(\frac{4}{3}\right)\right)$

$m≔\mathrm{abs}\left(3+4\mathrm{I}\right)$

$m≔5$

$\mathrm{ar}≔\mathrm{argument}\left(3+4\mathrm{I}\right)$

$\mathrm{ar}≔\arctan \left(\frac{4}{3}\right)$

$\mathrm{polar}\left(m\,\mathrm{ar}\right)$

$\mathrm{polar}\left(5\,\arctan \left(\frac{4}{3}\right)\right)$

$\mathrm{polar}\left(3\mathrm{I}\right)$

$\mathrm{polar}\left(3\,\frac{\mathrm{\pi }}{2}\right)$

$\mathrm{polar}\left(a+b\mathrm{I}\right)$

$\mathrm{polar}\left(\left|a+\mathrm{I}b\right|\,\arg \left(a+\mathrm{I}b\right)\right)$

$\mathrm{map}\left(\mathrm{evalc}\,\right)$

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

$\mathrm{polar}\left(-3\,\frac{\mathrm{\pi }}{2}\right)$

$\mathrm{polar}\left(\mathrm{-3}\,\frac{\mathrm{\pi }}{2}\right)$

$\mathrm{polar}\left(4.\,\mathrm{\pi }\right)$

$\mathrm{polar}\left(4.\,\mathrm{\pi }\right)$

$\mathrm{polar}\left(0\right)$

$\mathrm{polar}\left(0\,0\right)$

${\mathrm{polar}\left(r\,t\right)}^2\mathrm{polar}\left(s\,u\right)$

${\mathrm{polar}\left(r\,t\right)}^2\mathrm{polar}\left(s\,u\right)$

$\mathrm{simplify}\left(\right)$

$\mathrm{polar}\left(r^{2}s\,2t+u\right)$