If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω²)¹⁰⁰ + (1 - ω + ω²)¹⁰⁰ equal to?  

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 $\rm Z_1^2+Z_2^2+Z_1Z_2=0$