Find all circles which are orthogonal to `|z|=1and|z-1|=4.`

Find all integers lambda for which the system of equations x+2y - 3z = 1,2x - lambday - 3z = 2x+2y + lambda z = 3 has a unique solution.

Show that all the roots of the equation a_(1)z^(3)+a_(2)z^(2)+a_(3)z+a_(4)=3, (where|a_(i)|le1,i=1,2,3,4,) lie outside the circle with centre at origin and radius 2//3.

Let z_(1),z_(2) and z_(3) be three non-zero complex numbers and z_(1) ne z_(2) . If |{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0 , prove that (i) z_(1),z_(2),z_(3) lie on a circle with the centre at origin. (ii) arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(2) .

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

Find all the roots of the equation : (3z -1)^4+(z-2)^4 =0 in the simplified form of a + ib.

The centre of circle represented by |z + 1| = 2 |z - 1| in the complex plane is

Find the maximum and minimum values of |z| satisfying |z+(1)/(z)|=2

Find the gratest and the least values of |z_(1)+z_(2)|, if z_(1)=24+7iand |z_(2)|=6," where "i=sqrt(-1)

If z_1, z_2, z_3 are complex numbers such that |z_1|= |z_2|= |z_3| =|1/z_1+1/z_2+1/z_3|=1, |z_1+z_2+z_3| is :

If two complex numbers z_1,z_2 are such that |z_1|= |z_2| , is it then necessary that z_1 = z_2 ?