Show that a branch (Sec. 33) log ::: = In r + iO ( r > 0.

Complex Variables and Applications | 9th Edition | ISBN: 9780073383170 | Authors: James Ward Brown

ISBN: 9780073383170 169

Solution for problem 3.26 Chapter Chapter 3

Complex Variables and Applications | 9th Edition

Textbook Solutions
2901 Step-by-step solutions solved by professors and subject experts
Get 24/7 help from StudySoup virtual teaching assistants

Complex Variables and Applications | 9th Edition

4 5 1 265 Reviews

Problem 3.26

Show that a branch (Sec. 33) log ::: = In r + iO ( r > 0. a < 0 < u + 27 ) of the logarithmic function can be written log:= - ln(r + y-) + i tan- :_ I , , 1 ( r) 2 x in rectangularcoordinates. Then. using the theorem in Sec. 23. show that the given branch is analytic in its domain of delinition and that there. cl 1 -log:::= - cl::: - :::

Step-by-Step Solution:

Step 1 of 3

9/30/2017 F52B11D1E32842A3A06460D2D35AE776.png https://mail.google.com/mail/u/0/#inbox/15ed44902ae5e6e9projector=1 1/1 9/30/2017 7587F72FDA9C439081F2279D0C7F4DC2.png https://mail.google.com/mail/u/0/#inbox/15ed44902ae5e6e9projector=1 1/1 9/30/2017 DE03D1C24D07434088E93FB94AEB0DBA.png

Step 2 of 3