- #1
kukumaluboy
- 61
- 1
Homework Statement
The Attempt at a Solution
-1 < (z-w) /(1-z*w) < 1
[/B]
Hi can give clue. I am clueless
Solving Complex Number Inequalities
- Thread starter kukumaluboy
- Start date
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Homework Help Overview
The discussion revolves around solving inequalities involving complex numbers, specifically the expression -1 < (z-w) /(1-z*w) < 1. Participants are exploring the implications of comparing complex numbers using inequalities.
Discussion Character
- Exploratory, Assumption checking, Mixed
Approaches and Questions Raised
- Some participants question the validity of comparing complex numbers with inequalities. Others suggest using absolute values to reformulate the problem. There are discussions about simplifying the problem and the potential use of substitutions. One participant expresses uncertainty about the type of questions encountered in their exams.
Discussion Status
The discussion is active, with participants offering hints and suggestions for approaching the problem. There is a recognition of the complexity involved, and multiple interpretations of the problem are being explored. Some guidance has been provided regarding the use of absolute values and the potential for simplification.
Contextual Notes
Participants note that they have not encountered similar questions in their previous exams, which adds to their uncertainty. There is also mention of the possibility of using real and imaginary parts to analyze the problem further.
-1 < (z-w) /(1-z*w) < 1
[/B]
Hi can give clue. I am clueless
- #2
mfb
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You cannot compare complex numbers with inequalities.kukumaluboy said:
Hint: ##| \frac{a}{b} | = \frac{|a|}{|b|}##
- #3
kukumaluboy
- 61
- 1
|z-w| < |1-z*w| ?? should i square both sides?
- #4
mfb
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I would simplify the problem a bit before.
How comfortable are you with substitutions?
I think this problem is solvable without, but it makes life easier if you can simplify it first.
How comfortable are you with substitutions?
I think this problem is solvable without, but it makes life easier if you can simplify it first.
- #5
kukumaluboy
- 61
- 1
Honestly. we have never done these type of questions before. Our exams are always set with questions that we have nvr done before. This is a past year paper haha. Can teach me the one without the substitution ?
- #6
mfb
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Well, repeating equations you had before would be pointless, right?kukumaluboy said:
You can write both z and w in terms of real and imaginary part, square both sides and see what you get. It gets much easier if you get rid of one of the four parameters before, however. You can multiply both sides by |z*/z|, that should work.
Edit: Forget the multiplication, it is not as complicated as I expected with the longer approach.
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