Algebra Level 5

$$\displaystyle x^{4} + ax^{3} + bx^{2} + cx + d = 0$$

With $$a,b,c,d \in \mathbb R$$

Has 4 non real roots, two with the sum $$3 + 4i$$ and the other two with product $$13 + i$$.

Then find the value of b.