Proofs for Complex Inequalities to Bound a Complex Integral

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SUMMARY

The discussion centers on proving two complex inequalities: |1-z|/|z|<2 and |1+z|/|z|>1/2. Initially, the user incorrectly asserts the inequalities can be proven, but upon further clarification, acknowledges they are false for specific values of z. The user ultimately seeks to demonstrate these inequalities as bounds for a complex integral as z approaches infinity.

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  • Understanding of complex analysis and limits
  • Familiarity with complex integrals
  • Knowledge of inequalities in mathematical proofs
  • Experience with asymptotic behavior of functions
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  • Study the behavior of complex functions as z approaches infinity
  • Learn about bounding techniques in complex analysis
  • Explore the properties of complex integrals and their convergence
  • Investigate the use of inequalities in mathematical proofs
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Mathematicians, students of complex analysis, and researchers working on complex integrals and inequalities.

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Hi,

I need two simple proofs of complex inequalities.

1) |1-z|/|z|<2

2)|1+z|/|z|>1/2

Ik need them for a bound of a complex integral.It's not homework

Thank you
 
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Both inequalities are false, hence cannot be proven.

Try z=0.1 in (1).
Try z=-1 in (2).
 
Hi,

yes you are right.

But it's my fault,I forgot something.

I have to show this inequalities for z->infinity as a lower and upper bound in a complex

integral.

Sorry
 

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