TIFR2021-Maths-A: 15

Question

Which one of the following statements is correct?

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