{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

exam_2_m3364_summer_2011_v1_0

# exam_2_m3364_summer_2011_v1_0 - Exam 2 Math 3364 Summer...

This preview shows page 1. Sign up to view the full content.

Exam 2: Math 3364 Summer 2011 Problem 1. (10) Is the function f defined by f ( z ) = f ( x + iy ) = e 2 x cos( y )+ i (2 e 2 x sin( y )) analytic on the complex plane C ? Justify your answer. Problem 2. (5 each, 10 total) Find all solutions of the following equations. It is possible that at least one of these equations has no solutions. (a) e iz = 2. (b) cos( z ) = i sin( z ). Problem 3. (10) Sketch the image of the semidisk { z C : | z | 1 , 0 Arg( z ) π } under the map G ( z ) = e iπ/ 2 z + 1. Problem 4. (3 each, 18 total) For each of the following statements, determine if the statement is always true or not always true. (a) If f ( z ) and g ( z ) are analytic on C , then f ( z ) g ( z ) is analytic on C . (b) If f ( z ) and g ( z ) are analytic on C , then f ( z ) /g ( z ) is analytic on C . (c) If f ( z ) is differentiable at z 0 , then f ( z ) is continuous at z 0 . (d) If f ( z ) is continuous at
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online