Prove that for every complex number $\displaystyle z$ it happens that:

$\displaystyle |z + 10| + |z + 11| + |z + 19| \le|z + 8| + |z + 12| + |z + 20|$

- Jun 15th 2008, 09:27 PMmathwizardChallenging: Prove the following property of complex numbers.
Prove that for every complex number $\displaystyle z$ it happens that:

$\displaystyle |z + 10| + |z + 11| + |z + 19| \le|z + 8| + |z + 12| + |z + 20|$