The roots of x2 - () + 34 are 5 ± 3i.

What do you mean by " () "?

Let's check the roots and see what middle term results. We must multiply here:

If 5+3i is a root, then x-5-3i is a factor. Also, if 5-3i is a root, then x-5+3i is a factor.

We must multiply together (x-5-3i) (x-5+3i).

One way of doing this is as follows: [ (x-5) + 3i][ (x-5) - 3i]

Recalling that (a+b) (a-b) = a^2 - b^2,

[ (x-5) + 3i][ (x-5) - 3i] becomes (x+5) ^2 + 9, which

can be expanded and simplified as follows:

x^2 + 10x + 25 + 34

So, your " () " in your " x^2 - () + 34" should be "10x + 25."

In summary, the roots of x^2 + 10x + 25 + 34 are 5+3i and 5-3i.