Article usage: "in (/the/a) polar form"

Here are three sentences:

I can write [some imaginary number] *in polar form*.
Trigonometric functions are used *in the polar form* of imaginary numbers.
You can also represent a point on a graph in a polar form.

The third is a bit subtle. "In polar form" would work and would probably be used with an audience familiar with the idea of polar coordinates. But for an audience to whom polar forms are a new concept, at least as applied to the problem at hand, the "a" acknowledges that novelty. It's like the difference between "You can use GPS for that" and "You can use a GPS for that." The first tells you that the problem can be solved using a technology with which you are familiar, the second that the problem can be solved using tech with which you may not be familiar.