The parallelogram law.

The identity is called the parallelogram law because if we think of z and w as vectors (or points) in the plane, then it tells us that the sum of the squares of the lengths of the sides of a parallelogram is equal to the sum of the squares of the lengths of its diagonals.

To prove the identity, just write

displaymath21

displaymath23

displaymath25

The last equality follows from tex2html_wrap_inline27 .

Similarly, we have

displaymath29

Adding these gives the identity.

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Author: Michael O'Neill

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