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

The last equality follows from .

Similarly, we have

Adding these gives the identity.

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