quick complex number questions

Hi

Need help on the following:

1)if z is any cube root of unity then 1+z+z^2 must be.

A - 0

B - 1

C - 3

D - 0 or 3

E - 1 or 3

2) For any complex numbers z with conjugate $\displaystyle \overline{z}$, which of the following is not necessarily true?

A - $\displaystyle |z|=|\overline{z}|$

B - $\displaystyle \frac{z}{\overline{z}}$ is real

C - $\displaystyle \frac{z}{\overline{z}}$ is real

D - $\displaystyle z+\overline{z}$ is real

E - $\displaystyle |z/\overline{z}|$ is real

P.S