Given that are distinct fifth roots of unity, evaluate the expression above.
If is monic cubic polynomial having roots . Then evaluate topmost expression modulo 17.
If , then find the value of
If find
The equation has three solutions, one of which is real and the other two are non-real complex numbers. Determine the number and type of solutions of
Note: When is a complex number different from , and is a real number, can have more than one possible value. In this case, we assume that the complex number is a solution of the equation where is a given real number, if at least one of the values of is equal to