If `1,Z_1,Z_2,Z_3,........Z_(n-1)` are `n^(th)` roots of unity then the value of `1/(3-Z_1)+1/(3-Z_2)+..........+1/(3-Z_(n-1))` is equal to

If 1,z_1,z_2,z_3,.......,z_(n-1) be the n, nth roots of unity and omega be a non-real complex cube root of unity, then prod _(r=1)^(n-1) (omega-z_r) can be equal to

Find the minimum value of |z-1 if ||z-3|-|z+1||=2.

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If the complex numbers z_(1), z_(2)" and "z_(3) denote the vertices of an isoceles triangle, right angled at z_(1), " then "(z_(1)-z_(2))^(2)+(z_(1)-z_(3))^(2) is equal to

If z_(1) = 2 - i and z_(2) = -4 + 3i, find the inverse of z_(1)z_(2) and (z_(1))/(z_(2)) .

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to a. 1 b. 3 c. 5 d. 7

Find the greatest and the least value of |z_1+z_2| if z_1=24+7ia n d|z_2|=6.

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals: