How do you solve a complex number problem

Find real values of the number a for which a. i is a solution of the polynomial equation ... u, v and w are the three roots of the equation z3 - 1 = 0 ... Calculate all solutions of |z-1|.|z-1|=1 ... The equation z3 - (n + i) z + m + 2 i = 0 ... Let z' the conjugate complex number of z.