結合されたテキストに基づいて質問をする
以下は、数学論文の1つのパッセージです：

"The fundamental theorem of algebra states that every polynomial equation with complex coefficients has at least one complex root. This result is surprising, as it implies the existence of complex numbers that cannot be expressed using only real numbers. The proof of this theorem involves complex analysis and topology, and requires a deep understanding of both fields. A key step in the proof is to show that every non-constant polynomial with complex coefficients can be factored into linear factors over the complex numbers."
1. What does the fundamental theorem of algebra state?
2. Why is the result of the fundamental theorem of algebra surprising?
3. What fields are involved in the proof of the fundamental theorem of algebra?
4. What is a key step in the proof of the fundamental theorem of algebra?