= Solution
In an orthonormal <computational basis>, the squared <norm> is the sum of the squared <moduli> of the coefficients:
$$
\langle\phi|\phi\rangle=\left|\frac{\sqrt3}{2}\right|^2+\left|\frac{1+i\sqrt3}{4}\right|^2
=\frac34+\frac{1+3}{16}=\boxed{1}.
$$
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>.
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