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Math Help - prove problem

  1. #1
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    prove problem

    please help me with this prove problem

    z1/z2+z3 <= |z1|/||z2|-|z3|| ; |z2|<>|z3|, z=x+iy

    thanks.
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  2. #2
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    Quote Originally Posted by unicorn
    please help me with this prove problem

    z1/z2+z3 <= |z1|/||z2|-|z3|| ; |z2|<>|z3|, z=x+iy

    thanks.
    There is an impossibility in your problem.
    The right hand side is a real number because of absolute value ffor complex numbers, but the left hand remains a complex number. How can a complex number be ordered?
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  3. #3
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    excuse me! the problem is:
    |z1/z2+z3| <= |z1|/||z2|-|z3|| ; |z2|<>|z3|, z=x+iy
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  4. #4
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    Quote Originally Posted by unicorn
    excuse me! the problem is:
    |z1/z2+z3| <= |z1|/||z2|-|z3|| ; |z2|<>|z3|, z=x+iy
    If you mean:

    Prove that \forall z_1, z_2, z_3 \in \mathbb{C}:

    \frac{|z_1|}{|z_2+z_3|} \le \frac{|z_1|}{|\ |z_2|-|z_3|\ |}?

    Then it is sufficient to prove that:

    |z_2+z_3| \ge  |\ |z_2|-|z_3|\ |

    RonL
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  5. #5
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    maybe it's silly, but how can I prove that
    <br />
|z_2+z_3| \ge |\ |z_2|-|z_3|\ |<br />
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