Demonstration for Re(z), Im(z), Abs(z) and Arg(z)

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Homework Help Overview

The discussion revolves around the mathematical representations of complex numbers, specifically focusing on the real part, imaginary part, absolute value, and argument of a complex number, denoted as Re(z), Im(z), Abs(z), and Arg(z). Participants are exploring the validity of certain equations and seeking demonstrations of these concepts.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the derivations of the formulas for Re(z), Im(z), Abs(z), and Arg(z). Some suggest expressing z in different forms, such as x + iy or r e^{iθ, to facilitate understanding. Others question the complexity of proving Arg(z) compared to Re(z) and seek clarification on the standard representation of complex numbers.

Discussion Status

The discussion is ongoing, with participants providing hints and suggestions rather than direct solutions. There is a recognition of the need for the original poster to show their work, and some participants express frustration over perceived evasiveness in responses. Multiple interpretations of the problem are being explored, particularly regarding the nature of mathematical demonstrations.

Contextual Notes

Participants note that the forum rules require showing work for homework-related questions, which has led to some tension in the discussion. The original poster has expressed dissatisfaction with previous responses received in other topics.

Jhenrique
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Someone can demonstrate me why

##Re(z) = \frac{1}{2} \left ( z+\bar{z} \right )##
##Im(z) = \frac{1}{2i} \left ( z-\bar{z} \right )##
##Abs(z)=\sqrt{z\bar{z}}##
##Arg(z)=-i ln\left ( \frac{z}{\sqrt{z\bar{z}}} \right )##

?

2# Is correct to affirm that

##Arg(z)=-i ln\left (\sqrt{\frac{z}{\bar{z}}} \right)##

?
 
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Try writing ##z## as either ##x + iy## or ##r e^{i\theta}##, whichever is most suitable in each case. If you get stuck somewhere, please show what you tried.
 
Jhenrique said:
Someone can demonstrate me why

##Re(z) = \frac{1}{2} \left ( z+\bar{z} \right )##
##Im(z) = \frac{1}{2i} \left ( z-\bar{z} \right )##
##Abs(z)=\sqrt{z\bar{z}}##
##Arg(z)=-i ln\left ( \frac{z}{\sqrt{z\bar{z}}} \right )##

?

2# Is correct to affirm that

##Arg(z)=-i ln\left (\sqrt{\frac{z}{\bar{z}}} \right)##

?

PF Rules require you to show your work. We do not do homework here; we just give hints and suggestions.
 
Ray Vickson said:
PF Rules require you to show your work. We do not do homework here; we just give hints and suggestions.

homework? no comments...

I'm asking for a demonstration. Demonstration in math is a serious thing.
 
Jhenrique said:
homework? no comments...

I'm asking for a demonstration. Demonstration in math is a serious thing.
That's not relevant. If the question is about homework or textbook problems, the rules here require that you show what you have tried.
 
I find it odd that the OP is asking for proof for the representation of Arg(z) as well as Re(z). The difference in difficulty between the two of these is quite profound.Start with answering these questions:
What is the standard representation for z, a complex number? Hint: It's already been said in this thread.
What is Re(z) equal to? What about Im(z)?
What is [itex]\bar{z}[/itex]?
 
I already show my hypotheses a lot of times in others topics but, in general, the answer that I have received are, nearly always, a specie of subterfuge. If someone ask how much is 2+2 the answers are (in general) "the sum was the first discovery of man...", "the equality is reflexive, replacement, transitive, symmetric..." etc,etc,etc. But the answer 2+2 is equal to 2 not is given.
 
Jhenrique said:
I already show my hypotheses a lot of times in others topics but, in general, the answer that I have received are, nearly always, a specie of subterfuge. If someone ask how much is 2+2 the answers are (in general) "the sum was the first discovery of man...", "the equality is reflexive, replacement, transitive, symmetric..." etc,etc,etc. But the answer 2+2 is equal to 2 not is given.
No wonder, because 2 + 2 ≠ 2.

Since you have refused to show any sort of effort on this problem, I am closing this thread.
 

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