Extending Polynomial Identities to Complex Numbers Practice Test

A student wants to verify that polynomial operations (expanding and simplifying) work the same way over complex numbers. Which option correctly computes $(2+3i)^2$ using $$(a+b)^2=a^2+2ab+b^2$$ with $a=2$ and $b=3i$?

Use polynomial identities over complex numbers to factor $x^4+4$ completely over $\mathbb{C}$. (Hint: $x^4+4=(x^2)^2- (2i)^2$.) Which option gives a correct complete factorization into linear factors?