Complex numbers questions

So I missed the last week of class because I've been sick and with my textbooks stuck in my school lockers, I can't really get caught up on work. My friend was able to send me two sample questions they've been learning in class, but I have no idea what it means? Can someone please explain and teach me how to solve these questions?

Unsure of the notation too, the second z in the first question has a line over it, I don't think it's supposed to be z hat, but that's all I know.

1) Find the complex number z such that $\displaystyle (2+i)z + (4-i)\hat{z} = -1 + 5i$.

2) If $\displaystyle u=-3 + 2i$ and $\displaystyle v = 3 + 5i$ are complex numbers, calculate the modulus of $\displaystyle \frac{u}{v}$.

(Also, is modulus supposed to be like the programming modulus operation, or is it related? (i.e. 15 mod 10 = 5))

Thanks a lot, guys!