please help me with this prove problem

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

thanks.

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- May 16th 2006, 01:08 AMunicornprove problem
please help me with this prove problem

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

thanks. - May 16th 2006, 06:13 AMThePerfectHackerQuote:

Originally Posted by**unicorn**

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? - May 17th 2006, 06:51 AMunicorn
excuse me! the problem is:

|z1/z2+z3| <= |z1|/||z2|-|z3|| ; |z2|<>|z3|, z=x+iy - May 17th 2006, 10:27 AMCaptainBlackQuote:

Originally Posted by**unicorn**

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

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

Then it is sufficient to prove that:

$\displaystyle |z_2+z_3| \ge |\ |z_2|-|z_3|\ |$

RonL - May 18th 2006, 05:27 AMunicorn
maybe it's silly, but how can I prove that

$\displaystyle

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

$