Q: Show u = x²-y² is harmonic. Find its harmonic conjugate. uₓ = 2x, uₓₓ = 2; u_y = -2y, u_yy = -2. uₓₓ+u_yy = 0 ✓ HARMONIC! Conjugate v: v_y = uₓ = 2x → v = 2xy+g(x). vₓ = 2y+g' = -u_y = 2y: g' = 0. v = 2xy! f = u+iv = z² ✓!