Do they satisfy? (Part 2)

See Part 1 first if you haven't tried it.

$P$ : Algebraic numbers

1. $2014^{2014}$

2. $2 + \sqrt{2}$

3. $3 + 5i$

4. $\pi$

5. $e$

6. $\frac{1}{2}(1 + \sqrt{3}i)$

7. $\sum_{k = 1}^{\infty}10^{-k!}$

8. $2^{\sqrt{2}}$