Complexification of a real vector space

Let V be a complex vector space, with conjugation . Prove that a subspace W of V is the complexification of a real vector space S iff W is close under

Haven't a clue how to work this one.

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Originally Posted by dwsmith

Let V be a complex vector space, with conjugation . Prove that a subspace W of V is the complexification of a real vector space S iff W is close under

Haven't a clue how to work this one.

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It's closed under everything except for possibly the multiplication by complex scalars. Now, how precisely do we define to and ?