If z is a non-zero complex number, prove that |conjugate(z) + 1/z| >=2
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. Using we obtain .
Last edited by FernandoRevilla; July 15th 2011 at 10:00 AM.
Would you please derive more detail why modulus(z)^2 + 2 + 1/modulus(z)^2 >= 4? Many thanks.
Originally Posted by tinng Would you please derive more detail why modulus(z)^2 + 2 + 1/modulus(z)^2 >= 4? Many thanks. What does the graph of look like ....? What is its range ....? (Have you learned calculus and therefore know how to find coordinates of turning points?)
Originally Posted by tinng Would you please derive more detail why modulus(z)^2 + 2 + 1/modulus(z)^2 >= 4? Another way, prove that . The last inequality is trivially satisfied.
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