 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/ib/paper-2/10g/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

For nonnegative integers

m, n

⟨ z^{m}, z^{n} ⟩ = \frac{1}{2 π} \int_{0}^{2 π} e^{i (m - n) θ} d θ = δ_{mn} .

1, z, z^{2}, z^{3}, \dots is an orthonormal basis of P .

This is an algebraic basis: no infinite linear combinations are needed in the polynomial vector space.

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