Consider the equation $Z^{200}-\lambda Z^{199}+1=0$ . Let $Z_1,Z_2,Z_3\mathrm{...}{Z}_{200}$  be non-zero complex numbers and $Z^{200}-\lambda Z^{199}+1=(Z-Z_1)(Z-Z_2)(Z-Z_3)\mathrm{...}(Z-Z_{200})$  then

Real part of  $\sum _{j=1}^{200}\sum _{k=1}^{200}\frac{Z_j}{Z_k}$ is 1

Real part of $\sum _{j=1}^{200}\sum _{k=1}^{200}\frac{Z_j}{Z_k}$  is 0 

Imaginary part of  $\sum _{j=1}^{200}\sum _{k=1}^{200}\frac{Z_j}{Z_k}$  is 1

Imaginary part of $\sum _{j=1}^{200}\sum _{k=1}^{200}\frac{Z_j}{Z_k}$  is 0