# How to prove polarization identity?

How to prove polarization identity? For any $u, v \in V$ $4 \langle T(u), v \rangle = \langle T(u+v), u+v \rangle - \langle T(u-v), u-v \rangle + i\langle T(u+iv), u+iv \rangle - i\langle T(u-iv), u-iv \rangle$

-
What did you try? –  AD. Nov 4 '10 at 13:57
What is the property of the $\langle . , . \rangle$ operator? $\langle u, v + w \rangle = ...$ (Hint: in the real case, we speak about bilinear forms). –  Djaian Nov 4 '10 at 13:59
As a side comment: you've posted 11 questions on this forum so far, most of them are homework type questions with initially incorrectly applied tags (this one also, which I'll fix in a minute). You may get better attention if you at least tag questions in the correct field. You may also garner more good will if you actually accept answers. At least 3 or 4 of the questions you've asked in the past month have received very nice answers which you've ignored. –  Willie Wong Nov 4 '10 at 14:02
@AD. : I think you can delete the "What" in your question. –  Djaian Nov 4 '10 at 14:03
@Djaian: nice joke! :D –  Ｊ. Ｍ. Nov 4 '10 at 14:06
show 1 more comment

Expand RHS, using distributive property and the property that $\langle u,cv\rangle=\bar{c}\langle u,v\rangle$. Simplify and cancel many terms to get the LHS.