If the equation `z^4+a_1z^3+a_2z^2+a_3z+a_4=0` where `a_1,a_2,a_3,a_4` are real coefficients different from zero has a pure imaginary root then the expression `(a_3)/(a_1a_2)+(a_1a_4)/(a_2a_3)` has the value equal to

If a_1,a_2, a_3, a_4 be the coefficient of four consecutive terms in the expansion of (1+x)^n , then prove that: (a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)dot

If a_1,a_2,.....a_n are in H.P., then the expression a_1a_2 + a_2a_3 + ... + a_(n-1)a_n is equal to

Let A be the set of 4- digit numbers a_1a_2a_3a_4 where a_1gt a_2 gt a_3 gt a_4 then n(A) is equal to

If z_1,z_2,z_3 are any three roots of the equation z^6=(z+1)^6, then arg((z_1-z_3)/(z_2-z_3)) can be equal to

If z_1, z_2 are complex number such that (2z_1)/(3z_2) is purely imaginary number, then find |(z_1-z_2)/(z_1+z_2)| .

If the fourth roots of unity are z_1,z_2,z_3,z_4 then z_1^2+z_2^2+z_3^2+z_4^2 is equal to

If a_ngt1 for all ninN ,then log_(a_2)a_1+log_(a3)a_2+.....+log_(an)a_(n-1)+log_(a1)a_n has the minimum value

If A, A_1,A_2,A_3 are the areas of the inscribed and escribed circles of a DeltaABC, then

If the coefficients of four consecutive terms in the expansion of (1+x)^n are a_1,a_2,a_3 and a_4 respectively. then prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2a_2/(a_2+a_3).

If z_1 + z_2 + z_3 + z_4 = 0 where b_i in R such that the sum of no two values being zero and b_1 z_1+b_2z_2 +b_3z_3 + b_4z_4 = 0 where z_1,z_2,z_3,z_4 are arbitrary complex numbers such that no three of them are collinear, prove that the four complex numbers would be concyclic if |b_1b_2||z_1-z_2|^2=|b_3b_4||z_3-z_4|^2 .