complex variable Problems (108-3)

(See attached file for full problem description) --- - flow around a corner... - components of velocity... --- (See attached file for full problem description)

complex variable problems (108-4)

(See attached file for full problem description) --- - Show the speed of the fluids... - At an interior point of a region of flow... --- (See attached file for full problem description)

Complex Variable Question

(See attached file for full problem description) --- Find the image of the semi-infinite strip x > 0, 0 < y < 2 when w = iz + 1. Sketch the strip and its image. --- (See attached file for full problem description)

Function analytic at origin

Assume that f(z) is analytic at the origin and f(0) = first derivative of f at 0 = 0. Prove that f(z) can be written in the form f(z) = [z^2]g(z), where g(z) is analytic at z = 0.

Function analytic in the open disk

Let g be continuous on the real interval [0,1] and define H(z) := integral (from 0 to 1) [g(t)/(1-z[t^2])]dt, (|z| < 1) Prove that H is analytic in the open disk |z| < 1.