Show that the equation `a z^3+b z^2+ barb z+ bara =0` has a root `alpha` such that `|alpha|=1,a ,b ,za n dalpha` belong to the set of complex numbers.

Show that the equation a z^3+b z^2+ barb z+ bara =0 has a root alpha such that |alpha|=1,a ,b ,z and alpha belong to the set of complex numbers.

Show that the equation a z^3+b z^2+ barb z+ bara =0 has a root alpha such that |alpha|=1,a ,b ,z and alpha belong to the set of complex numbers.

Show that the equation az^(3)+bz^(2)+bar(b)z+bar(a)=0 has a root alpha such that | alpha|=1,a,b,zand alpha belong to the set of complex numbers.

The equation az^(3) + bz^(2) + barbz + bara = 0 has a root alpha , where a, b,z and alpha belong to the set of complex numbers. The number value of |alpha|

The equation az^(3) + bz^(2) + barbz + bara = 0 has a root alpha , where a, b,z and alpha belong to the set of complex numbers. The number value of |alpha|

If alpha is a complex constant such that alpha z^2+z+bar( alpha)=0 has a real root, then

If alpha is a complex constant such that alpha^(2)+z+bar(alpha)=0 has a real root then

The roots z_(1),z_(2),z_(3) of the equation z^(3)+3 alpha z^(2)+3 beta z+gamma=0 correspond to the points A,B and C on the complex plane.Find the complex number representing the centroid of the triangle ABC, and show that the triangle is equilateral if alpha^(2)=beta

If alpha is a complex constant such that alpha z^2+z+ baralpha=0 has a real root, then (a) alpha+ bar alpha=1 (b) alpha+ bar alpha=0 (c) alpha+ bar alpha=-1 (d)the absolute value of the real root is 1

If alpha is a complex constant such that alpha z^2+z+ baralpha=0 has a real root, then (a) alpha+ bar alpha=1 (b) alpha+ bar alpha=0 (c) alpha+ bar alpha=-1 (d)the absolute value of the real root is 1