Part 2/5:
We begin by considering one of the cube roots ( z ), expressed as ( \sqrt[3]{Z} ). By applying the cube roots of unity, we can generate three solutions for the variable ( z ):
The principal cube root, denoted as ( z_1 ), which is equal to ( \sqrt[3]{Z} ).
The second solution, ( z_2 ), is represented as ( z_1 \times W_1 ), where ( W_1 ) is one of the cube roots of unity.
Finally, the third solution, ( z_3 ), is derived as ( z_1 \times W_2 ), introducing the last cube root of unity into our calculations.