Show that $\mathbb{R}\oplus\mathbb{R}$ is not ring isomorphic to $\mathbb{C}$. Show that $\mathbb{R}\oplus\mathbb{R}$ is not ring isomorphic to $\mathbb{C}$.  
This is my first abstract algebra class and therefore if the explanation could be kept as simple as possible that would be very much appreciated. I dont even know how to approach this problem.

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*Nontrivial direct sums always have zero divisors, and $\mathbb C$ doesn't.

*$\mathbb C$ has other algebraic properties that $\mathbb R\oplus \mathbb R$ doesn't have, like existence of solutions to polynomial equations, which would be preserved under ring isomorphism.  For example, $\mathbb R\oplus \mathbb R$ has no element whose square is $(-1,-1)$, whereas $z^2=-1$ does have solutions in $\mathbb C$.

