# prove problem

• May 16th 2006, 01:08 AM
unicorn
prove problem

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

thanks.
• May 16th 2006, 06:13 AM
ThePerfectHacker
Quote:

Originally Posted by unicorn

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?
• May 17th 2006, 06:51 AM
unicorn
excuse me! the problem is:
|z1/z2+z3| <= |z1|/||z2|-|z3|| ; |z2|<>|z3|, z=x+iy
• May 17th 2006, 10:27 AM
CaptainBlack
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 $\displaystyle \forall z_1, z_2, z_3 \in \mathbb{C}$:

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

Then it is sufficient to prove that:

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

RonL
• May 18th 2006, 05:27 AM
unicorn
maybe it's silly, but how can I prove that
$\displaystyle |z_2+z_3| \ge |\ |z_2|-|z_3|\ |$