Answer
$\left( {2\sqrt 5 ,5.8195} \right)$
Work Step by Step
$$\eqalign{
& {\text{We have the rectangular coordinates }}\left( {x,y} \right) = \left( {4, - 2} \right) \cr
& {\text{The polar coordinates are:}} \cr
& r = \sqrt {{x^2} + {y^2}} \cr
& r = \sqrt {{{\left( 4 \right)}^2} + {{\left( { - 2} \right)}^2}} \cr
& r = 2\sqrt 5 \cr
& \tan \theta = \frac{{ - 2}}{4} \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{ - 2}}{4}} \right) \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{ - 2}}{4}} \right) + 2\pi \approx 5.8195 \cr
& {\text{Therefore}}{\text{, the polar coordinate is:}} \cr
& \left( {2\sqrt 5 ,5.8195} \right) \cr} $$