If `z_1, z_2, z_3, z_4,` are the non-real complex fifth roots of unity, then the sum of coefficient in the expansion of `(3 + z_1x + z_2x^2 +z_3x^3 +z_4x^4)^5` is

The coefficient of x^2y^4z^2 in the expansion of (2x - 3y + 4z)^9 is

The coefficient of x^(2)y^(4)z^(2) in the expansion of (2x-3y+4z)^(9) is

If z_1,z_2,z_3,z_4 are imaginary 5th roots of unity, then the value of sum_(r=1)^(16)(z1r+z2r+z3r+z4r),i s 0 (b) -1 (c) 20 (d) 19

If z_1,z_2,z_3,z_4 are imaginary 5th roots of unity, then the value of sum_(r=1)^(16)(z1r+z2r+z3r+z4r),i s 0 (b) -1 (c) 20 (d) 19

If z_(1),z_(2),z_(3) andz_(4) are the roots of the equation z^(4)=1, the value of sum_(i=1)^(4)zi^(3) is

If z is a non real cube root of unity, then (z+z^(2)+z^(3)+z^(4))^(9) is equal to

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then prove that z_1, z_2, z_3, z_4 are concyclic.