If w= -1-i 3 2 where i= -1 , then the value of | array ccc 1 & w & w^2 w & w^2 & 1 w^2 & 1 & w array | is

Step-by-step solution

aligned & = -1- i 3 2 , ^2= 1-3+2 i 3 4 = -1+ i 3 2 , & ^3=1, ^6=1 & | array ccc 1 & & ^2 & ^2 & 1 ^2 & 1 & array | & =1 ( ^3-1 )- ( ^2- ^2 )+ ^2 ( - ^4 ) & =1 ( ^3-1 )+0+ ^2 ( - ^4 ) . aligned aligned & = ^3-1+ ^3- ^6 & =2 ^3- ^6-1 & =2(1)-1-1 & =0 aligned