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polar

convert to polar form

 Calling Sequence polar(z) polar(r, t)

Parameters

 z - expression r - expression, understood to be real t - expression, understood to be real

Description

 • 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.

Examples

 > $\mathrm{polar}\left(3+4I\right)$
 ${\mathrm{polar}}{}\left({5}{,}{\mathrm{arctan}}{}\left(\frac{{4}}{{3}}\right)\right)$ (1)
 > $\mathrm{convert}\left(3+4I,\mathrm{polar}\right)$
 ${\mathrm{polar}}{}\left({5}{,}{\mathrm{arctan}}{}\left(\frac{{4}}{{3}}\right)\right)$ (2)
 > $m≔\left|3+4I\right|$
 ${m}{≔}{5}$ (3)
 > $\mathrm{ar}≔\mathrm{argument}\left(3+4I\right)$
 ${\mathrm{ar}}{≔}{\mathrm{arctan}}{}\left(\frac{{4}}{{3}}\right)$ (4)
 > $\mathrm{polar}\left(m,\mathrm{ar}\right)$
 ${\mathrm{polar}}{}\left({5}{,}{\mathrm{arctan}}{}\left(\frac{{4}}{{3}}\right)\right)$ (5)
 > $\mathrm{polar}\left(3I\right)$
 ${\mathrm{polar}}{}\left({3}{,}\frac{{\mathrm{\pi }}}{{2}}\right)$ (6)
 > $\mathrm{polar}\left(a+bI\right)$
 ${\mathrm{polar}}{}\left(\left|{a}{+}{I}{}{b}\right|{,}{\mathrm{arg}}{}\left({a}{+}{I}{}{b}\right)\right)$ (7)

If  a and b  are intended to be real, map evalc onto this expression:

 > $\mathrm{map}\left(\mathrm{evalc},\right)$
 ${\mathrm{polar}}{}\left(\sqrt{{{a}}^{{2}}{+}{{b}}^{{2}}}{,}{\mathrm{arctan}}{}\left({b}{,}{a}\right)\right)$ (8)
 > $\mathrm{polar}\left(-3,\frac{\mathrm{Pi}}{2}\right)$
 ${\mathrm{polar}}{}\left({-3}{,}\frac{{\mathrm{\pi }}}{{2}}\right)$ (9)
 > $\mathrm{polar}\left(4.,\mathrm{Pi}\right)$
 ${\mathrm{polar}}{}\left({4.}{,}{\mathrm{\pi }}\right)$ (10)
 > $\mathrm{polar}\left(0\right)$
 ${\mathrm{polar}}{}\left({0}{,}{0}\right)$ (11)
 > ${\mathrm{polar}\left(r,t\right)}^{2}\mathrm{polar}\left(s,u\right)$
 ${{\mathrm{polar}}{}\left({r}{,}{t}\right)}^{{2}}{}{\mathrm{polar}}{}\left({s}{,}{u}\right)$ (12)
 > $\mathrm{simplify}\left(\right)$
 ${\mathrm{polar}}{}\left({{r}}^{{2}}{}{s}{,}{2}{}{t}{+}{u}\right)$ (13)

 See Also