Extending Polynomial Identities to Complex Numbers Practice Test

Over $\mathbb{C}$, the sum of squares factors using $a^2+b^2=(a+bi)(a-bi)$. Using this idea, which is a correct factorization of $x^2+16$ over the complex numbers?

Use the identity $a^2-b^2=(a+b)(a-b)$ with complex numbers to compute $(1+i)^2-(2-i)^2$ by factoring. Which result is correct?