Given the complex number Z, find Z + Z square + Z three square + Can we use the summation formula of real number equal ratio sequence to sum?

Given the complex number Z, find Z + Z square + Z three square + Can we use the summation formula of real number equal ratio sequence to sum?

Sn = Z + Z ^ 2 + Z ^ 3 +... + Z ^ n, zsn = Z ^ 2 + Z ^ 3 +... + Z ^ 4 +... + Z ^ (n + 1). By subtracting the two formulas, we get (1-z) Sn = (Z + Z ^ 2 + Z ^ 3 +... + Z ^ n) - [Z ^ 2 + Z ^ 3 +... + Z ^ 4 +... + Z ^ (n + 1)] = Z + (Z ^ 2-z ^ 2) + (Z ^ 3-z ^ 3) +... (Z ^ N-Z ^ n) - Z ^ (n + 1) = Z-Z ^ (n + 1), so Sn = [Z-Z ^ (n + 1)] / (1-z) =