This question deals with the upper half plane model of hyperbolic geometry. Points are represented by complex numbers with positive imaginary component. Let P = −2 + 7i,Q = 3 + 2i and R = 3 + 8i be points in the hyperbolic plane. (i) Determine the unique hyperbolic lines joining the pair of points Q and R and the pair P and Q. (ii) Calculate the hyperbolic distances: h(Q, R) between Q and R, and h(P,Q), between P and Q.
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