I'm having trouble with the problem below.
Plot on an Argand diagram and deduce that
I plotted them and the tangent of the resulting argument was indeed , but I have no idea how to show that it is equal to . I've been staring blankly at it for an hour now, I know I'm going to kick myself when I see how it's done! :P
Let O be the point representing z = 0, let A be the point representing , let B be the point representing and let C be the point representing .
Consider the triangles OAB and OBC. Angle OBA (why?). Therefore angle OBC .
But triangle OBC is isoscles (why?). Therefore angle COB = OCB (why?).
Therefore angle COA . Voila!