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.

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|

Solve the equation z^2 +|z|=0 , where z is a complex number.

If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus of 'z' is

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

Find the centre and radius of the circle formed by all the points represented by z = x + iy satisfying the relation |(z-alpha)/(z-beta)|= k (k !=1) , where alpha and beta are the constant complex numbers given by alpha = alpha_1 + ialpha_2, beta = beta_1 + ibeta_2 .

If z = cos alpha + i sin alpha then the amplitude of z^2+barz is:

If the equation ax^2 + bx + c = 0, 0 < a < b < c, has non real complex roots z_1 and z_2 then

If the complex numbers z_1,z_2,z_3 represents the vertices of a triangle ABC, where z_1,z_2,z_3 are the roots of equation z^3+3alphaz^2+3alphaz^2+3betaz+gamma=0, alpha,beta,gamma beng complex numbers and alpha^2=beta then /_\ABC is (A) equilateral (B) right angled (C) isosceles but not equilateral (D) scalene

z_(1) and z_(2) are the roots of the equaiton z^(2) -az + b=0 where |z_(1)|=|z_(2)|=1 and a,b are nonzero complex numbers, then

A root of unity is a complex number that is a solution to the equation, z^n=1 for some positive integer nNumber of roots of unity that are also the roots of the equation z^2+az+b=0 , for some integer a and b is