Two complex number problems!

Because it's my first post on this forum, I would like to thank everyone who contributed to create such a wonderful forum.

I have to solve this two problems:

1. **Find** $\displaystyle Re(z)=?$ $\displaystyle Im(z)=?$

if:

$\displaystyle z=\sqrt[3]{\frac{2}{-\sqrt{2+i\sqrt{2}}}}$

For first problem i don't have a clue how to come to a solution.

** 2. Find ** $\displaystyle |z+1|+z+i=0$

I know that $\displaystyle |Z|=\sqrt{x^2+y^2}$ but, what is $\displaystyle |z+1|$?

Thank you very much and sorry for my english.