Prove that V is a vector space with the operations

Show that the set of complex number C={x+iy|x and y are real, i2=-1} is a vector space. Verify each axiom.

Show that (a + b)(v + w) = av + aw + bv + bw for any v, w ∈ V and any a, b ∈ F. Hint: The proof will require you to use both distributive properties of a vector space. All are vectors except a

If {v1, V2, V3} is an orthogonal set of nonzero vectors in an inner product space V, that {v1, v2, V3} is linearly independent. then prov