Let W be subspace of a vector space V. Prove that if $\displaystyle V= W \bigoplus W^c. $ and T is orthogonal projection onto W, then T=T*.

$\displaystyle V= W \bigoplus W^c. $ is direct sum
$\displaystyle W^c $ is W complement
T* is T transpose conjugate.

I know:
$\displaystyle V= W \bigoplus W^c $ means
$\displaystyle v= w_1+w_2$, st $\displaystyle w_1 \in W_1$ and $\displaystyle w_2 \in W^c $
$\displaystyle T(w_1+w_2)= T(w_1)=w_1 $

Not sure how to make T=T*?

Thanks in advance