If ar = cos 2rπ/9 +i sin 2rπ/9 , r = 1, 2, 3,…, i = √ -1 then the determinant

Question

If a_r = cos\(\cfrac{2r\pi}{9}+i\,sin\cfrac{2 r\pi}{9}\)

a_r = cos 2rπ/9 +i sin 2rπ/9 , r = 1, 2, 3,…, i = √ -1 then the determinant 

(1) a₂a₆\(-\)a₄a₈

(2) a₉

(3) a₁a₉\(-\)a₃a₇

(4) a₅

Answer 1

Correct answer is: (3) a₁a₉\(-\)a₃a₇