The polar coordinate system

This is not a math tutorial. See Why am I writing about math?

The Wikipedia Polar coordinate system page seems especially good (accessed on January 19, 2026).

The polar coordinate system uses distance and angle to indicate where a point is on a plane (“to specify a point on a plane”):

• distance: the point’s distance from the pole
• angle: the point’s direction from the pole, relative to the direction of the polar axis

For now I’ll consider the pole to be the equivalent of the point (0, 0) on the Cartesian plane.

I’ll assume that the polar axis is a line drawn from the pole at the equivalent of y=0 on the Cartesian plane. ($\theta = 0$ in the polar coordinate system).

I’ll assume that as the angle ($\theta$) increases, the point moves in a counter clockwise direction away from the polar axis.

References

Wikipedia contributors. “Polar coordinate system.” Accessed on: January 19, 2026. https://en.wikipedia.org/wiki/Polar_coordinate_system#Complex_numbers .