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A complex Complex inequality

  1. Aug 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Let b and a be two complex numbers. Prove that
    |1+ab| + |a + b| ≥ √(|a²-1||b²-1|).

    2. Relevant equations
    Complex algebra

    3. The attempt at a solution
    I don't know how to proceed. I posted it here to get some ideas :p
  2. jcsd
  3. Aug 4, 2014 #2


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    Try factoring the left hand side:
    $$|a^2 - 1||b^2 - 1| = |(a-1)(a+1)(b-1)(b+1)|$$
    Now see what happens if you rearrange the factors and recombine them.
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