What is the value of the sum $\rm \sum\limits_{n=1}^{20}(i^{n-1}+i^n+i^{n+1})$ where i = √-1 ?

Direction : Consider the following for the items that follow :  

Let Z ₁  and Z ₂  be any two complex numbers such that $\rm Z_1^2+Z_2^2+Z_1Z_2=0$

Direction : Consider the following for the items that follow :  

Let Z ₁  and Z ₂  be any two complex numbers such that $\rm Z_1^2+Z_2^2+Z_1Z_2=0$

If $z$ is any complex number and $i z^3+z^2-z+i=0$, where $i=\sqrt{-1}$, then what is the value of $(|z|+1)^2$ ?