._72Re^162 থেকে._(z_1)X^(A_1)+ আলফা কণা ._74W^(188) থেকে._(Z_2)Y^(A_2)+বিটা কণার মান

._72Re^162 to._(z_1)X^(A_1)+ alpha particle ._74W^(188)to._(Z_2)Y^(A_2) +Beta particle value of (A_2-A_1)/(Z_2-Z_1) is :

Prove that Re (z_ (1) z_ (2)) = Re z_ (1) Rez_ (2) -Im z_ (1) Im z_ (2)

If z_(1),z_(2) are complex number such that Re(z_(1) ) = |z_(1) - 1| , Re(z_(2)) = |z_(2) -1| and arg(z_(1) - z_(2)) = (pi)/(3) , then Im (z_(1) + z_(2)) is equal to

Find the coefficient of x in the determinant |((1+x)^(a_1 b_1),(1+x)^(a_1 b_2),(1+x)^(a_1 b_3)),((1+x)^(a_2 b_2),(1+x)^(a_2 b_2),(1+x)^(a_2 b_3)),((1+x)^(a_3 b_3),(1+x)^(a_3 b_2),(1+x)^(a_3 b_3))|=0.

If z_(1)=2-i,quad +2=-2+i, find :Re((z_(1)z_(2))/(z_(1)))

If a_1, a_2, a_3..... a_n in R^+ and a_1.a_2.a_3.........a_n = 1, then minimum value of (1+a_1 + a_1^2) (1 + a_2 + a_2^2)(1 + a_3 + a_3^2)........(1+ a_n + a_n^2) is equal to :-

If z_1 + z_2 + z_3 = A, z_1 + z_(2)omega+ z_(3)omega^(2)= B, z_1 + z_(2) omega^(2) + z_(3) omega=C where 1, omega, omega^2 are the cube roots of unity, then

The equation A/(x-a_1)+A_2/(x-a_2)+A_3/(x-a_3)=0 where A_1,A_2,A_3gt0 and a_1lta_2lta_3 has two real roots lying in the invervals. (A) (a_1,a_2) and (a_2,a_3) (B) (-oo,a_1) and (a_3,oo) (C) (A_1,A_3) and (A_2,A_3) (D) none of these

If z_(1)=a+ib and z_(2)=c+id are complex numbers such that Re(z_(1)bar(z)_(2))=0, then the |z_(1)|=|z_(2)|=1 and Re(z_(1)bar(z)_(2))=0, then the pair ofcomplex nunmbers omega=a+ic and omega_(2)=b+id satisfies

If (a_2 a_3)/(a_1 a_4) = (a_2 + a_3)/(a_1 + a_4) = 3 ((a_2 - a_3)/(a_1 - a_4)) then a_1, a_2, a_3, a_4 are in