Question

How do you convert `-729` to polar form?

Answer 1

`-729 = 729 \ e^{i pi}` magnitude 729, angle `pi`.

Explanation:

I'll write numbers in polar form as `Re^{i theta}`, meaning magnitude `R`, angle `theta`. If you haven't gotten to that notation in class yet (from Euler's Formula), think of it as the polar coordinate pair `(R, theta)`.

`-729` has magnitude `729` and angle `pi` aka `180^circ`. The fact that negative reals have angle `pi` is the true meaning of Euler's Identity, `e^{i \pi}=-1.`

`-729 = 729 \ e^{i pi}`

That's `(729, 180^circ)` if that's how you write polar coordinates.