Past exam of the computer science course of the University of Oxford / 2021 / Quantum information / 1 / a / i / Solution

In an orthonormal computational basis, the squared norm is the sum of the squared moduli of the coefficients:Thus the vector is normalized and represents a pure state of a qubit. The imaginary part contributes positively to the squared modulus; squaring the coefficient without complex conjugation would give the wrong norm.