Find the equation of the geodesic in the hyperbolic upper half-plane joining -1+ with 1+i. Hint: You have to define a curvey: R {z E C|z > 0} so that y is a geodesic and (a) = 1 + i, y(b) 1+i for some a, b E R. You need not compute these a, b! = Exploit symmetry. Look at the ideal endpoints.