What is the Cartesian form of #( -1, (4pi)/3 ) #?
We are given the polar form, so there is a radius and an angle. We want to convert to
So we can use Euler's formula (or at least the idea behind it) to convert between Cartesian and polar:
From that, we just plug in the numbers, remembering our unit circle:
You could also notice that a negative radius is the same as adding or subtracting
which I think is a bit easier to think about.
The Cartesian coordinates
hence, the Cartesian coordinates are