If the roots of `(z-1)^n=i(z+1)^n` are plotted in an Argand plane, then prove that they are collinear.

If z^4= (z-1)^4 then the roots are represented in the Argand plane by the points that are

If the roots of (z-1)^(n)=2w(z+1)^(n) (where n>=3o* w complex cube root of unity are plotted in argand plane,these roots lie on

If the points z_(1),z_(2),z_(3) are the vertices of an equilateral triangle in the Argand plane, then which one of the following is not correct?

Prove that the equations , |(z-1)/(z+1)| = constant and amp ((z-1)/(z+1)) = constant on the argand plane represent the equations of the circle wich are orthogonal .

The roots of the equation z^(n)=(z+3)^(n)

If |z-1|=1, where is a point on the argand plane, show that (z-2)/(z)=i tan (argz),where i=sqrt(-1).

Z_(1)!=Z_(2) are two points in an Argand plane.If a|Z_(1)|=b|Z_(2)|, then prove that (aZ_(1)-bZ_(2))/(aZ_(1)+bZ_(2)) is purely imaginary.

If A(z_(1)) and A(z_(2)) are two fixed points in the Argand plane and a point P(z) moves in the Argand plane in such a way that |z-z_(1)|=|z-z_(2)| , then the locus of P, is

Show that the roots of equation (1+z)^n=(1-z)^n are i tan (rpi)/n, r=0,1,2,,…………,(n-1) excluding the vlaue when n is even and r=n/2