Factorization of the ring $\mathbb{Z} [i]$ of Gaussian Integers

Question

Prove that if a pair of integers a and b is a solution to the equation $$x^2 +y^2=n$$

Then $n$ factors $\mathbb{Z} [i]$ as the product $(a+bi)(a-bi)$

I understand that in $\mathbb{Z} [i]$ that $a^2 +b^2 = (a-bi)(a+bi)$. Im not sure how or what Im actually trying to prove.