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> **Possible Duplicate:**  
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> [AC in group isomorphism between R and R^2](https://mathoverflow.net/questions/25375/ac-in-group-isomorphism-between-r-and-r2) 
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Somewhere, I recall being told that there is an isomorphism between $\mathbb{R}$ and $\mathbb{C}$ under addition. However, despite a rather lengthy search, I have been unable to find anything to support this fact, although Paul Yale of Pomona College, in his paper, "Automorphisms of the Complex Numbers," showed that there are "wild" automorphisms of $\mathbb{C}$ that require the axiom of choice to construct. Given that rather surprising fact, it does not seem too unlikely that there could be an isomorphism between $\mathbb{R}$ and $\mathbb{C}$. So, the question is: Is it possible for there to be an isomorphism between $\mathbb{R}$ and $\mathbb{C}$, and if so, what is is? 



Is there an Isomorphism between R and C under addition?
As vector spaces over the rationals, they have the same dimension, so the only tricky part is the difficulty in finding a basis. 


