Suppose z₁, z₂ and z₃ are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If z₁ = 1 + i\(\sqrt { 3 } \) then find z₂ and z₃.

Find all cube roots of \(\sqrt { 3 } +i\)

Solve the equation z³+ 8i = 0, where \(z \in \mathbb{C}\)

Simplify: (1+i)¹⁸

Simplify: \(\left( -\sqrt { 3 } +3i \right) ^{ 31 }\)