In an Argand diagram O is the origin, P represents the number 7 – i and Q represent the number 12 + 4i.
Calculate the size of angle OPQ.
I’ve done 1st part but how can I calculate angle OPQ in this case?
What's the first part?
I'd call the point P(7, -1) and Q(12, 4) and use them as vectors based at the origin. Then use the dot product to get the angle.
The other way is a bit messier: put each point into the form $\displaystyle r~e^{i~\theta}$. The find the difference in the arguments.
-Dan
Fro any two non-zero complex numbers z & w the angle between them can be found by: $\displaystyle \Theta = \arccos \left( {\frac{{{\mathop{\rm Re}\nolimits} (z){\mathop{\rm Re}\nolimits} (w) + {\mathop{\rm Im}\nolimits} (z){\mathop{\rm Im}\nolimits} (w)}}{{\left| z \right|\left| w \right|}}} \right) $