MATH 345 Midterm: MATH 345 Amherst F14M345

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 345
• Professor: All

Document Summary

Explain: prove or disprove the following statements. (a) zw = z w. |f (z)|2 = 4 |z|2 on d: for the function f (z) = , what is the type of singularity at z = 1: suppose that an entire function f = u + iv is blessed with the additional property that ux + vy = 0 throughout the complex plane. Z f (z) f (z) dz = 0: suppose that f (z) is analytic in the annulus r < |z| < for some xed r > 0 so that there is a convergent series. Xk=1 valid for all z in the annulus. We de ne the residue at of f (z) as. 1 f (z)dz f (z) = akzk + bk zk for any r > r. here the curve cr(0) is the negatively oriented circle of radius r centered at z = 0.