Let V be an inner product space over the complex numbers C with the inner product defined as (u,v〉 = Σ 1 uvi for any vectors u (u₁, U2,..., Un) and v = (V₁, V2, .. ‚vn) in V. Given the vectors a = (1 + i, 2 − 2i, —i) and b = (2 — i, -i, 3) in V, (a) Calculate the inner product (a, b). (b) Find the norm of a using the inner product.

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