x^2+225 ..factor over complex numbers?

how about

(x+15i)(x-15i) ?

sounds good to me

go back down to the fraction one i have a ?

To factor the expression x^2 + 225 over complex numbers, we can use the factoring method for quadratic equations. However, it's important to note that the given expression x^2 + 225 does not have any real solutions since the discriminant (b^2 - 4ac) is negative. Therefore, it is necessary to factor the expression over complex numbers.

To start, we rewrite the expression as (x^2 + 15^2). Notice that this expression is in the form of a^2 + b^2. In the complex number system, we know that a^2 + b^2 can be factored as (a + bi)(a - bi), where i is the imaginary unit (i^2 = -1).

Therefore, applying the factoring formula, we have:

(x^2 + 15^2) = [(x + 15i)(x - 15i)]

So, the expression x^2 + 225 factors over complex numbers as (x + 15i)(x - 15i).