According to the formula from another problem, [r , θ]ⁿ = [rⁿ, nθ]. If [r⁴, 4θ] = [1+√3, 0], then $\displaystyle r=\sqrt[4]{1+\sqrt{3}}$. You need to find all 0 ≤ θ < 2π such that 4θ is an integer multiple of 2π.
Well, the idea is the same, only now $\displaystyle r=\sqrt[4]{|a|}$ and you need to find all 0 ≤ θ < 2π such that 4θ equals arg(a) up to an integer multiple of 2π