Geometric Interpretations..

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July 2nd 2008, 12:13 AM
kalagota

Geometric Interpretations..

can someone give geometric interpretations on this..

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

thanks..
July 2nd 2008, 12:45 AM
Isomorphism

Quote:

Originally Posted by kalagota

can someone give geometric interpretations on this..

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

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?
July 2nd 2008, 01:02 AM
flyingsquirrel

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Quote:

Originally Posted by kalagota

can someone give geometric interpretations on this..

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

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

You can find it here.

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