n. a pair of coordinates, generally written (r, θ) or [r, θ], that locate a point in a plane by means of the length, r, of the line joining the point to the origin or pole, and the angle, θ, swept out by that line from a single axis. As is apparent from the figure below, the polar coordinates of the point whose Cartesian coordinates are (x, y) areso that in the Argand diagram, this point represents the complex number x + iy, where r and θ are respectively the modulus and amplitude (or anomaly or azimuth) of the complex number; conversely, the Cartesian coordinates of (r, θ) are
(x, y) = (rsin θ, rcos θ).
Compare spherical coordinates. P is the point (r, θ).