The roots of the quadratic equation $z^2 + az + b = 0$ are $2 - 3i$ and $2 + 3i$. what is $a+b$?

We know for our problem that the zeroes of our quadratic equation are  and , which means that the solutions for our equation are  and . We are going to use those solutions to express our quadratic equation in the form ; to do that we will use the zero factor property in reverse:








Now, we can multiply the left sides of our equations:

= 
= 
= 
Now that we have our quadratic in the form , we can infer that  and ; therefore, we can conclude that .