" 19.On simplification "(1)/(1+z^(a-b)+z^(ac))(1)/(1+z^(b-c+z^(b)a))(1)/(1+z^(-a)+z^(c-b))" would reduces to "

(1)/(1+z^(a-b)+z^(a-c))(1)/(1+z^(b-c)+z^(b-a))(.1)/(1+z^(c-a)+z^(c-b)) would reduce to

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

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|= 2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

If x = (a-b)/(a+b) , y = (b-c)/(b+c), z = (c-a)/(c+a) , " then " ((1-x)(1-y)(1-z))/((1+x)(1+y)(1+z)) is equal to

If a^(x)=b^(y)=c^(z) and b^(2)=ac prove that (1)/(x)+(1)/(z)=(2)/(y)