How exactly do I do these questions:

1. z = 1 + $\displaystyle \sqrt{3}$ . Find the smallest positive integer n for which $\displaystyle z^n$ is real and evaluate $\displaystyle z^n$ for this value of n. Show that there is no integral value of n for which $\displaystyle z^n$ is imaginary.

2. Find the modulus of $\displaystyle \frac{7-i}{3-4i}$. Evaluate $\displaystyle tan[\arctan\frac{4}{3} - \arctan\frac{1}{7}]. $Hence, find the principal argument of $\displaystyle \frac{7-i}{3-4i}$ in terms of $\displaystyle \pi$.