If z^2 + 1 = 0, find z^(49) + z^(50) + z^(51) + z^(52).
z^49 + z^50 + z^51 + z^52 =
z^49 + z^51 + z^50 + z^52
z^49 ( 1 + z^2) + z^50 ( 1 +z^2)
z^49 ( z^2 + 1) + z^50 ( z^2 + 1) =
z^49 (0) + z^50 (0) =
0
