Algebraic Number Theory, Lesson 2: Number Fields

In this second lesson of my series on algebraic number theory, I define and discuss number fields, i.e., fields of algebraic numbers, and provide some examples.

[davesmathchannel-tsik]

I made a couple mistakes on the last slide. As it turns out, i√2 is NOT a primitive element of the number field ℚ(√2, i), but √2 + i is a primitive element. The other mistake I made is that the primitive cube root of unity is ω = (-1 + √-3)/2, not (1 + √-3)/2.

[theshoulderofgiants]

8:25 in the 4th example
why is it Q(cube_root_of_2)
why don't we also include cube_root_of_4 in the shorthand...it doesn't seem to be a typo as you mention something about not having to include it..why not?? aren't we losing information about the 3rd coefficient ??