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)? 

If $z=\frac{1+i √{3}}{1-i √{3}}$ where i = √-1 then what is the argument of z ?

If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then what is |z| equal to ?