Is vector addition possible without Cartesian coordinates?

Question

Suppose I need to add some vectors of which I know the magnitude and direction. The result I need is the magnitude and direction of the final vector. I've been taught to do this:

polar -> cartesian -> (vector addition) -> cartesian -> polar

That is tedious. Is there a process to add vectors without finding the Cartesian components?

polar -> (vector addition) -> polar

Answer 1

If you're willing to extend your definition of "algebraically" to "I can punch it into my calculator", check the phasor addition section of

http://en.wikipedia.org/wiki/Phasor

It's basically a polar coordinate.