Solutions and Answer Manual for Basic Complex Analysis

a₂ analytic function arctan bounded branch Cauchy integral formula Cauchy-Riemann equations Cauchy's circle of radius closed curve closed disc complex numbers conformal map converges absolutely converges uniformly cosh cosh2y defined differentiable entire function f is analytic f is constant f is continuous f(z₁ f(z₂ f(zo finite gives goes harmonic function Hence Im(a imaginary inverse inverse function theorem Laplace transform lemma Let f Let f(z maximum modulus principle neighborhood one-to-one open set pole of order polynomial positive real axis problem Prove quadrant radius of convergence Re(z residue Review Exercises roots Section Show that f sin²x sine singularity sinh Suppose f unit circle unit disc x+iy Y₂ z-zo z|lz ау ди ду эх