Vectors in polar coordinates

[retoa]

Yes, I already use this solution when I only have to do vector addition (same problem on the 35s by the way) but this is the only thing you can do.
You can not do "dot" nor "cross" product, this does not exist for complex numbers.
Matrix multiplication (e.g. with a rotation matrix) will also not give the same result with complex numbers as with vectors (obviously).