In the following paper, http://www.math.uconn.edu/~kconrad/blurbs/galoistheory/cyclotomic.pdf, the author writes,
"For any field K, an extension of the form K(ζ), where ζ is a root of unity, is called a cyclotomic extension of K. The term cyclotomic means “circle-dividing,” which comes from the fact that the nth roots of unity in C divide a circle into n arcs of equal length."
Does this mean that the Complex Numbers form a Cyclotomic Field Extension of the Reals where n = 4? I was thinking this because 1,-1,i,-i would then divide the unit circle into 4 arcs of equal length.
I may, however, be misinterpreting the meaning of the term "nth roots of unity", so any clarification would be much appreciated.
Your interpretation is correct.