Is f(z)+i arg(z) an analytic function?

Click For Summary

Discussion Overview

The discussion centers on the analyticity of the function f(z) + i arg(z), exploring whether this function can be classified as analytic. Participants examine the relationship between this function and the logarithm function, particularly in the context of complex analysis.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the analyticity of the function f(z) + i arg(z) and requests an explanation.
  • Another participant asserts that the function relates to the definition of log(z), suggesting a connection to analyticity.
  • A participant seeks clarification on how to separate ln(z) and arg(z) to assess the analyticity of the function.
  • It is noted that log(z) is analytic in any simply connected domain that excludes 0, implying conditions under which the function may be analytic.
  • Additionally, a participant mentions that ln|z| represents the real logarithm, which may influence the discussion on analyticity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the analyticity of the function, and multiple viewpoints regarding the relationship between the function and the logarithm remain present.

Contextual Notes

There are unresolved aspects regarding the separation of ln(z) and arg(z) and the implications of their definitions on the function's analyticity. The discussion also highlights the importance of the domain in which log(z) is considered analytic.

Huns
Messages
3
Reaction score
0
Solve.jpg

Is this function analytic or not? Please explain
 
Physics news on Phys.org
Well, it's the definition of log(z).
 
Svein said:
Well, it's the definition of log(z).
so how to split ln (z) and arg (z) for determining analyticity?
 
Huns said:
so how to split ln (z) and arg (z) for determining analyticity?
log(z) is analytic in any simply connected domain that does not include 0.

By the way, the expression ln|z| is the real logarithm.
 

Similar threads

Undergrad Apparent counterexample to Cauchy-Goursat theorem (Complex Analysis)
  • · Replies 7 ·
Replies
7
Views
3K
True or false? |z|^2 is an entire function
  • · Replies 16 ·
Replies
16
Views
2K
C/C++ Interpolation of a rapidly oscillating function
  • · Replies 3 ·
Replies
3
Views
3K
[Complex analysis] Contradiction in the definition of a branch
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Bounding modulus of complex logarithm times complex power function
  • · Replies 4 ·
Replies
4
Views
4K
Engineering How do I draw the Bode diagram of this transfer function?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Topology - Boundary of a ball without a point
  • · Replies 5 ·
Replies
5
Views
3K
Is f(z) =(1+z)/(1-z) a real function?
  • · Replies 17 ·
Replies
17
Views
3K
MHB Differentiating Complex Square Root Function: Bruce P. Palka, Ex. 1.5, Ch. III
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Questions about the arg of complex numbers
  • · Replies 4 ·
Replies
4
Views
2K