Past exam of the physics A course of the University of Cambridge / 2015 / Paper 1 / Section A / 1

The Born rule uses the squared modulus, so the imaginary term contributes positively: $|a+ix{|}^2=a^2+x^2$. For $a>0$, wavefunction normalization would multiply the supplied expression by $N=\sqrt{3/(4a^3)}$. Equivalently, take the ratio of the integrals directly:Using ${\psi }^2$ instead of $|\psi {|}^2$ would fail to produce a real, nonnegative probability density.