#2028: Complex Numbers explain

[Cueball (the student) is raising his hand and writing with his other hand. He is sitting down at a desk, which has a piece of paper on it.]

Cueball: Does any of this really have to do with the square root of -1? Or do mathematicians just think they’re too cool for regular vectors?

[Miss Lenhart (the teacher) is standing in front of a whiteboard.]

Miss Lenhart: Complex numbers aren’t just vectors. They’re a profound extension of real numbers, laying the foundation for the fundamental theorem of algebra and the entire field of complex analysis.

[Miss Lenhart is standing slightly to the right in a blank frame.]

Miss Lenhart: And we’re too cool for regular vectors.

Cueball (off-screen): I knew it!