Calculus 2: Find the angle difference (in radians) between adjacent 4th roots.

Let z = e^(2π i /n). Then z^n = 1, and z is called an nth root of unity. There are n nth roots of unity,
equispaced around the unit circle; they have the form z = e^(2π i (k/n)), where k = 0, 1, 2, , n−1.
Of course 1 is an nth root of unity, for every n.

Draw the unit circle for the four 4th roots of unity.
The angle difference (in radians) between adjacent 4th roots is ____________?

(Unit circle drawing is not necessary. I just need the blank!)

"" the sixth roots
"" the eights roots


Please help! I am so confused! An explanation would be amazingggg!

Note that the angle is given by 2πk/n. Every time we increment k by 1, 2πk/n increments by 2π/n. Thus, the angle difference in radians between adjacent nth roots is 2π/n. So, the angle difference in radians between adjacent 4th roots is 2π/4 = π/2.

I hope this helps!