If , where is a complex number, then the value of
Explanation for the correct option.
Step 1. Find the roots of the equation.
The roots of the equation are complex cube roots of unity. So or .
The sum of roots is and the product of roots is .
Step 2. Write the given expression in terms of and find its value.
In the given espression substitute for .
Now, as so the equation can be written as:
Simplifying by using laws of exponent as:
Now as so the value can be found as:
So the value of the expression is .
Hence, the correct option is B.