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Which one of the following statements is correct?

  1. There Exists a $\mathbb{C}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$
  2. There exists no $\mathbb{C}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$, but there exists an $\mathbb{R}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$
  3. There exists no $\mathbb{R}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$, but there exists a $\mathbb{Q}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$
  4. None of the other three statements is correct
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