If `a_r=(cos2rpi+is in2rpi)^(1//9)` , then prove that `|a_1a_2a_3a_4a_5a_6a_7a_8a_9|=0.`

If a_r=(cos2rpi+i sin 2rpi)^(1//9) , then prove that |[a_1,a_2,a_3],[a_4,a_5,a_6],[a_7,a_8,a_9]|=0 .

If a_r=(cos2rpi+i sin 2rpi)^(19) , then prove that |[a_1,a_2,a_3],[a_4,a_5,a_6],[a_7,a_8,a_9]|=0 .

If a_r=(cos2rpi+isin2rpi)^((1)/(9)) , then the value of |{:(a_1,a_2,a_3),(a_4,a_5,a_6),(a_7,a_8,a_9):}| .

if a_(r) = (cos 2r pi + I sin 2 r pi)^(1//9) then prove that |{:(a_(1),,a_(2),,a_(3)),a_(4) ,,a_(5),,a_(6)),( a_(7),, a_(8),,a_(9)):}|=0

if a_(r) = (cos 2r pi + I sin 2 r pi)^(1//9) then prove that |{:(a_(1),,a_(2),,a_(3)),(a^(4) ,,a^(5),,a_(6)),( a_(7),, a_(8),,a_(9)):}|=0

If alpha_r=(cos2rpi+isin2rpi)^(1/10) , then |(alpha_1, alpha_2, alpha_4),(alpha_2, alpha_3, alpha_5),(alpha_3, alpha_4, alpha_6)|= (A) alpha_5 (B) alpha_7 (C) 0 (D) none of these

If alpha_r=(cos2rpi+isin2rpi)^(1/10) , then |(alpha_1, alpha_2, alpha_4),(alpha_2, alpha_3, alpha_5),(alpha_3, alpha_4, alpha_6)|= (A) alpha_5 (B) alpha_7 (C) 0 (D) none of these

If a_(r)="cos"(2rpi)/9+i "sin"(2rpi)/9 then value of the determinant Delta=|(1,a_(8),a_(7)),(a_(3),a_(2),a_(1)),(a_(6),a_(5),a_(4))| is

If Z_r=cos((2rpi)/5)+isin((2rpi)/5),r=0,1,2,3,4,... then z_1z_2z_3z_4z_5 is equal to

a_r={cos((2rpi)/9)+isin((2rpi)/9)} where r in {1,2,3 . . . 9} Find the value of abs((a_1,a_2,a_3),(a_4,a_5,a_6),(a_7,a_8,a_9))