find a regular expression and FA that each define $L_1 \cap L_2$ I am trying to find a regular expression and finite automaton that each define $L_1 \cap L_2$, where $L_1 = (ab^*)^*$ and $L_2 = b(a+b)^*$.

How would I start doing this problem?

So I would draw a FA and when I draw it I would have a complement meaning take anywhere you have a plus, get rid of it and anywhere you didn't have a plus add one in. Am I on the right track?
Hint: Every non-empty string in $L_1$ starts with $a$. Every string in $L_2$ starts with $b$.