If `a=omega!=1`, is a cube root of unity `b=785,c=2008i` and
`Delta=|(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c)|`
then `Delta` equals

Show that: |aa+ba+b+c2a3a+2b4a+3b+2c3a6a+3b10a+6b+3c|=a^(3)

Prove that |a a+b a+b+c2a3a+2B4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3

Suppose a,b,c epsilon R and Delta=|(a,a+b,a+b+c),(3a,4a+3b,5a+4b+3c),(6a,9a+6b,11a+9b+6c)| If Delta=11.728 then a=______

If omega (ne 1) is a cube root of unity and (1 + omega^(2))^(11) = a + b omega + c omega^(2) , then (a, b, c) equals

Using properties of determinants,prove that det[[a,a+b,a+b+c2a,3a+2b,4a+3b+2c3a,6a+3b,10a+6b+3c]]=a^(3)

If omega is a non-real cube root of unity, then Delta = |(a_(1) + b_(1) omega,a_(1) omega^(2) + b_(1),a_(1) + b_(1) + c_(1) omega^(2)),(a_(2) + b_(2) omega,a_(2) omega^(2) + b_(2),a_(2) + b_(2) omega + c_(2) omega^(2)),(a_(3) + b_(3) omega,a_(3) omega^(2) + b_(3),a_(3) + b_(3) omega + c_(3) omega^(2))| is equal to