All roots of the equation, `(1 + z)^6+ z^6= 0`(A) lie on a unit circle with centre at the origin

Let z_(1) , z_(2) be two roots of the equation z^(2) + az + b = 0 , z being complex . Further assume that the origin z_(1) and z_(2) form an equilateral triangle , then

All the roots of the equation x^(11) - x^(6) - x^(5) + 1 = 0 lie on a circle of radius __________.

If alpha = (z - i)//(z + i) show that, when z lies above the real axis, alpha will lie within the unit circle which has centre at the origin. Find the locus of alpha as z travels on the real axis form -oo "to" + oo

If alpha = (z - i)//(z + i) show that, when z lies above the real axis, alpha will lie within the unit circle which has centre at the origin. Find the locus of alpha as z travels on the real axis form -oo "to" + oo

All the roots of (z + 1)^(4) = z^(4) lie on

Let z_(1)" and "z_(2) be two roots of the equation z^(2)+az+b=0 , z being complex number further, assume that the origin, z_(1)" and "z_(2) form an equilateral triangle, then

Let z_(1),z_(2) be the roots of the equation z^(2)+az+12=0 and z_(1),z_(2) form an equilateral triangle with origin. Then the value of |a| is

Prove that, for integral value of n ge1 , all the roots of the equation nz^(n) =1 + z+ z^2 +….+z^(n) lie within the circle |z|=(n)/(n-1) .

The equation of the circle with centre (6,0) and radius 6 is