Show that $G: Z[t] → \mathbb{C}$ defined by $G(f)=f(\sqrt{-1})$ is a ring homomorphism with kernel $(t^2 + 1)$ and image the Gaussian integers. I'm clear about the ring homomorphism and image part. But I'm not sure how to formulate my language precisely about the statement of the kernel. 

For the kernel statement I suggest
With the kernel being the principal ideal generated by $t^2 + 1$
