Let V be a complex vector space and W a subset of V with the following properties:
(a) W is a real vector space with respect to the operations defined in V.
(b) For each α in V there exist unique vectors β, γ in W such that α=β+iγ.
Show that the equation Jα=β−iγ defines a conjugation on V such that Jα=α if and only if α belongs to W, and show also that J is the only conjugation on V with this property.