Question

Suppose p and q are points on the unit circle such that the line through p and q intersects the real axis. Show if z is the point where this line intersects the real axis, then z=(p+q)/(pq+1)

So far I've figured out that the equation for the line is z=p+t(q-p) but I don't know what to do with it.

Answer 1

In your equation, p and q are vectors

so, find where the y-component is zero.