5) Let P₂(C) be the vector space of polynomials with complex coefficients of degree ≤ 2, equipped with the inner product (ao + a₁x + a₂x², bo + b₁x + b₂x²) = aobo + a₁b₁ + a2b₂. Let f: P₂(C) → C be the linear transformation given by f(p) = -ip' (0) + (1 + i)p(0). Find the unique p = P₂(C) such that for all q = P₂(C), we have (q, p) = f(q).

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