(z + 1) ^ 4 + (z - 1) ^ 4 =
= (z ^ 2 + 2z + 1) ^ 2 + (z^2 - 2z + 1) ^ 2 =
= z ^ 4 + 4z ^ 2 + 1 + 4z ^ 3 + 2z ^ 2 + 4z + z ^ 4 + 4z ^ 2 + 1 - 4z ^ 3 + 2z ^ 2 - 4z =
= 2z ^ 4 + 12z ^ 2 + 2 = 1 <==> 2z ^ 4 + 12z ^ 2 = -1
2z ^ 4 >= 0 |
12z ^ 2 >= 0 | ==> 2zz ^ 4 + 12z ^ 2 =/= -1 ==> z nu are valori
