Prove that if f = f1(x) + i f2(x) and g = g1(x) + ig2(x) are vectors

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Prove that if f = f1(x) + i f2(x) and g = g1(x) + ig2(x) are vectors in complex C[a, b] then the formula
Prove that if f = f1(x) + i f2(x) and

defines a complex inner product on C[a, b].

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