Consider the following for the next items that follow:

Consider equation-I : z3 + 2z2 + 2z + 1 = 0 and equation-II : z1985 + z100 + 1 = 0.

What is the number of common roots of equation-I and equation-II?

If ω is a non-real cube root of 1, then what is the value of  $\left|\frac{1-\omega}{\omega+\omega^2}\right| ?$

If α and β are the distinct roots of equation x2 - x + 1 = 0, then what is the value of $\left|\frac{\alpha^{100}+\beta^{100}}{\alpha^{100}-\beta^{100}}\right|$ ?

If 2 - i√3 where i = √-1 is a root of the equation x2 + ax + b = 0, then what is the value of (a + b)?