rootsOfUnity

constexpr std::vector<Complex> rootsOfUnity(const int q) noexcept: Returns the roots of unity [1] for a positive integer \(q\).

Parameters

const int q

A positive integer denoting the power.

Returns

template<>
type std::vector<Complex>

A complex sequence. The list of the roots of unity.

The roots of unity are the complex numbers that satisfy the equation:

\[z^q = 1\]

The equation has the following \(q\) solutions:

\[1^{1/q} = e^{i2\pi (k/q)} \quad k = 0, \ldots, q-1,\]

Example

int q = 3;
std::vector<Complex> roots = rootsOfUnity(q); // Cube roots of unity
for(int i = 0; i < q; i++) {
    std::cout << roots[i] << "\n";
}

Output:

1 + 0j
-0.5 + 0.866025j
-0.5 - 0.866025j

References