Problem above. (Sorry I can't embed yet and the link seems to be removed when hyperlinked)
Fairly simple (I imagine) question that I am stuck on. The first two parts are fairly straightforward, however I am unsure on how to continue beyond that.
How does one find the roots given two roots? I've tried long dividing and resulted in nothing useful; any clever ideas?
Also for the final part, would the velocity merely be z'(t) and acceleration z''(t)? (after taking the complex conjugate of the denominator to turn it real)
Seems too easy to be the most numerously marked question, hence I feel like something is probably going wrong. Would I take the real parts of the velocity/acceleration after finding z' and z'' to find the magnitude? Or would it be a case of just finding the magnitude in the same sense as you would of an argand diagram (root of [x^2 + y^2]) simply with the variable t in place?
These questions were taken out of a Cambridge 'Maths for Natural Sciences' past exam question if any were curious