# Geometric Interpretations..

• Jul 2nd 2008, 12:13 AM
kalagota
Geometric Interpretations..
can someone give geometric interpretations on this..

$\displaystyle |z_1 + z_2|^2 + |z_1 - z_2|^2 = 2(|z_1|^2+|z_2|^2)$

thanks..
• Jul 2nd 2008, 12:45 AM
Isomorphism
Quote:

Originally Posted by kalagota
can someone give geometric interpretations on this..

$\displaystyle |z_1 + z_2|^2 + |z_1 - z_2|^2 = 2(|z_1|^2+|z_2|^2)$

thanks..

What exactly do you mean by geometric interpretation? Is it something like writing the above equation in the form of a geometrically meaningful statement?
• Jul 2nd 2008, 01:02 AM
flyingsquirrel
Quote:

Originally Posted by kalagota
can someone give geometric interpretations on this..

$\displaystyle |z_1 + z_2|^2 + |z_1 - z_2|^2 = 2(|z_1|^2+|z_2|^2)$

Geometrically it's an equation which links the sides of a parallelogram to its diagonals : $\displaystyle OC^2+OE^2=2(OA^2+AC^2)=\frac{1}{2}(OD^2+EC^2)$
• Jul 2nd 2008, 10:47 AM
ThePerfectHacker
You can find it here.