If `z_1,z_2,z_3` are three distinct non-zero complex numbers and `a ,b ,c in R^+` such that `a/(|z_1-z_2|)=b/(|z_2-z_3|)=c/(|z_3-z_1|),t h e n(a^2)/(z_1-z_2)+(b^2)/(z_2-z_3)+(c^2)/(z_3-z_1)i se q u a lto` `R e(z_1+z_2+z_3)` (b) `I mg(z_1+z_2+z_3)` `0` (d) None of these

If z_1, z_2, z_3 are distinct nonzero complex numbers and a ,b , c in R^+ such that a/(|z_1-z_2|)=b/(|z_2-z_3|)=c/(|z_3-z_1|) Then find the value of (a^2)/(z_1-z_2)+(b^2)/(z_2-z_3)+(c^2)/(z_3-z_1)

If z_1, z_2, z_3 are distinct nonzero complex numbers and a ,b , c in R^+ such that a/(|z_1-z_2|)=b/(|z_2-z_3|)=c/(|z_3-z_1|) Then find the value of (a^2)/(z_1-z_2)+(b^2)/(z_2-z_3)+(c^2)/(z_3-z_1)

If z_1, z_2, z_3 are distinct nonzero complex numbers and a ,b , c in R^+ such that a/(|z_1-z_2|)=b/(|z_2-z_3|)=c/(|z_3-z_1|) Then find the value of (a^2)/(z_1-z_2)+(b^2)/(z_2-z_3)+(c^2)/(z_3-z_1)

If z_(1),z_(2),z_(3) are three distinct non-zero complex numbers and a,b,c in R^(+) such that (a)/(|z_(1)-z_(3)|)=(b)/(|z_(2)-z_(3)|)=(c)/(|z_(3)-z_(1)|),quad then (a^(2))/(z_(1)-z_(2))+(b^(2))/(z_(2)-z_(3))+(c^(2))/(z_(2)-z_(1)) is equal to Re(z_(1)+z_(2)+z_(3))( b) Im g(z_(1)+z_(2)+z_(3))0(d) None of these

If z_(1),z_(2),z_(3) are distinct nonzero complex numbers and a,b,c in R^(+) such that (a)/(|z_(1)-z_(2)|)=(b)/(|z_(2)-z_(3)|)=(c)/(|z_(3)-z_(1)|) Then find the value of (a^(2))/(z_(1)-z_(2))+(b^(2))/(z_(2)-z_(3))+(c^(2))/(z_(3)-z_(1))

z_1,z_2,z_3 are complex number and p,q,r are real numbers such that: p/(|z_2-z_3|)= q/(|z_3-z_1|)= r/(|z_1-z_2|) . Prove that p^2/(z_2-z_3)= q^2/(z_3-z_1)= r^2/(z_1-z_2)=0

(a)/(|z_(1)-z_(2)|)=(b)/(|z_(2)-z_(3)|)=(c)/(|z_(3)-z_(1)|)(a,b,c in R) then (a^(2))/(|z_(1)-z_(2)|)=(b^(2))/(|z_(2)-z_(3)|)=(c^(2))/(|z_(3)-z_(1)|) is

If z_1,z_2,z_3 are three complex numbers such that |z_1|=|z_2|=|z_3|=1 , find the maximum value of |z_1-z_2|^2+|z_2-z_3|^2+|z_3+z_1|^2

If z_1,z_2,z_3 are three complex numbers such that |z_1|=|z_2|=1 , find the maximum value of |z_1-z_2|^2+|z_2-z_3|^2+|z_3+z_1|^2

If z_1,z_2,z_3 are complex number , such that |z_1|=2, |z_2|=3, |z_3|=4 , the maximum value |z_1-z_2|^(2) + |z_2-z_3|^2 + |z_3-z_1|^2 is :