Show that if d₁ d₂ dr R(z) = z-zt 2-22 z-Zr where each d, is real and positive and each z lies in the upper half-plane Im z > 0, then R(2) has no zeros in the lower half-plane Im z < 0. [HINT:Write R(2) = ++. Then sketch the vectors (z-z) for Im z> 0 and Bat Im z < 0. Argue from the sketch that any linear combination of these vectors with real, positive coefficients (dk/12-22) must have a negative (and hence nonzero) imaginary part. Alternatively, show directly that Im R(z) > 0 for Im z < 0.]