Given $z = 4 + 5i$ and $w = 3 + 7i$, first compute $2z$:

$2z = 2(4 + 5i) = 8 + 10i$

Then add $w$:

$2z + w = (8 + 10i) + (3 + 7i) = (8 + 3) + (10 + 7)i = 11 + 17i$