Can Complex Numbers Bridge the Gap Between Algebra and Geometry?

[nate9519]

This really isn't a homework question but I wasn't sure where to post it. I was watching a video by numberphile about complex numbers and the professer being interviewed said the most important thing about complex numbers is that they help bring algebra and geometry together. What did he mean by that?

 

[jedishrfu]

This article has some examples:

https://pcmi.ias.edu/files/Integrating Algebra and Geometry with Complex Numbers.pdf