Need help with complex number inequalities?

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SUMMARY

The discussion centers on solving complex number inequalities, specifically $$ 1 \leq z \overline {z} \leq 4 $$ and $$ |\Im(z)|<\Re(z) $$, where ##z## represents a complex number. Participants suggest that these inequalities are typical in complex analysis courses and can be approached using known properties of complex numbers. They emphasize that understanding the modulus and applying examples will clarify the inequalities without needing extensive resources.

PREREQUISITES
  • Understanding of complex numbers and their properties
  • Familiarity with complex analysis concepts
  • Knowledge of modulus and argument of complex numbers
  • Basic skills in solving inequalities
NEXT STEPS
  • Study the properties of complex numbers, focusing on modulus and conjugates
  • Explore complex analysis textbooks for sections on inequalities
  • Practice solving inequalities involving complex numbers
  • Learn about the geometric interpretation of complex inequalities
USEFUL FOR

Students in complex analysis courses, educators teaching complex number concepts, and anyone interested in mastering complex inequalities.

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Hi!

At university I have got a problem set with lots of inequalities. Unfortunately there are no explanations given how to do them. In Highschool we only did very easy inequalities.
Therefore I am looking for a resource for inequalities. Especially for more difficult inequalities like $$ 1 \leq z \overline {z} \leq 4 , |\Im(z)|<\Re (z),$$ where ##z## is a complex number.

I would be glad at any recommendations.
 
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what course are you taking where you find these inequalities? Complex analysis?
 
that looks like the kinds of problems you would do when first learning about complex numbers. the first one involves an identity with the modulus, and the second one looks almost self-explatory. just try a few examples where it's true & I think it will become clear. I don't think you need a whole book on inequalities if you're doing complex analysis & those are the problems you have. just apply what you know about complex numbers to find the regions where they're true.
 

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