For a complex number Z, if all the roots of the equation `Z^3 + aZ^2 + bZ + c = 0` are unimodular, then

For a complex number Z, if all the roots of the equation Z^3 + aZ^2 + bZ + c = 0 are unit modulus, then

If all the roots of the equation z^(4)+az^(3)+bz^(2)+cz+d=0(a,b,c,d in R) are of unit modulus,then

If a, b in C and z is a non zero complex number then the root of the equation az^3 + bz^2 + bar(b) z + bar(a)=0 lie on

For a complex number Z, if one root of the equation Z^(2)-aZ+a=0 is (1+i) and its other root is alpha , then the value of (a)/(alpha^(4)) is equal to

For a complex number Z, if one root of the equation Z^(2)-aZ+a=0 is (1+i) and its other root is alpha , then the value of (a)/(alpha^(4)) is equal to

If roots of the equation z^(2)+az+b=0 are purely imaginary then

If all the roots of z^(3)+az^(3)+bz+c=0 are of unit modulus,then

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then