The limit of the complex conjugate as z -> 0

Click For Summary

Discussion Overview

The discussion revolves around the behavior of the complex conjugate of a complex number as it approaches zero, specifically whether the limit of the complex conjugate of z approaches zero as z does. Additionally, participants explore the differentiability of the complex conjugate function and inquire about the limit of the principal logarithm as z approaches zero.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions whether the limit of the complex conjugate of z approaches zero as z approaches zero.
  • Another participant states that the map f(z) = conjugate of z is not differentiable and suggests proving this from the definition.
  • A participant inquires about calculating complex limits by separating them into real and imaginary parts, indicating this method simplifies the analysis.
  • Another participant asks about the limit of the principal logarithm as z approaches zero, indicating a related interest in complex limits.

Areas of Agreement / Disagreement

Participants express differing views on the differentiability of the complex conjugate function, and the inquiry into the limit of the principal logarithm introduces additional complexity. The discussion remains unresolved regarding the limit of the complex conjugate and the nature of its differentiability.

Contextual Notes

Participants have not fully explored the implications of their claims regarding differentiability and limits, and there may be missing assumptions regarding the definitions of the functions involved.

skriabin
Messages
11
Reaction score
0
Hi I'm wondering if the z- (complex conjugate of z) goes to zero as z does? Also what is the derivative of z- with respect to z? Thanks
 
Physics news on Phys.org
This is very important for me right now, so please if you know this, let me know... :)
 
The map f(z)= conjugate of z is not differentiable, and you should be able to prove this from the definition.

Do you know how to calculate complex limits by breaking them up into their real and imaginary parts? It makes looking at that limit very easy
 
Thank you. Got it.
 
While we're on the subject of complex limits, can anyone help me figure out what
<br /> \lim_{z\to 0} \text{Log } z<br />
is? (So we're talking about the principal logarithm here.)
 

Similar threads

Graduate Question about proof of Great Picard Theorem
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Existence of a limit implies that a function can be harmonic extended
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Expansion of a complex function around branch point
  • · Replies 3 ·
Replies
3
Views
3K
Complex conjugate of a pole is a pole?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Questions about the arg of complex numbers
  • · Replies 4 ·
Replies
4
Views
3K
How Can We Prove the Conjugate Transpose Property of Complex Matrices?
  • · Replies 5 ·
Replies
5
Views
2K
Understanding Complex Conjugates in QM (Griffiths pg. 13)
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How to take the spatial derivative of quaternions
  • · Replies 8 ·
Replies
8
Views
3K
Using Complex Conjugates to Decompose a Fraction
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Normal vector on complex function
  • · Replies 3 ·
Replies
3
Views
1K