# Help with hard complex numbers

We had the topic of complex numbers for my senior math team meet this week and i wasn't able to get two of the problems.

1.) $z=i^{\displaystyle \left(i^{\displaystyle \left(i^{(2)}\right)}\right)}$ and $a$ is the real part of $z$, find the lowest positive value of $\ln(a)$ [ i know it comes to $i-i$ but i don't know why that is e^(pi/2)]

2.) $$\left[\cos \left(\frac{2\pi}{7}\right) + \cos \left(\frac{4\pi}{7}\right) + \cos \left(\frac{8\pi}{7}\right)\right]^2$$ [I think i can use de moivre's forumla but i dont know how here]

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