Find the locus of complex number z, stisfying ` ( z + 1)^(n) = z^(n)`

Statement-1 : The locus of complex number z, satisfying (z-2)^(n) =z^(n) is a straight line . and Statement -2 : The equation of the form ax + by+c =0 in x -y plane is the general equation of striaght line.

Statement-1 : The locus of complex number z, satisfying (z-2)^(n) =z^(n) is a straight line . and Statement -2 : The equation of the form ax + by+c =0 in x -y plane is the general equation of striaght line.

Find the locus of a complex number z=x +yi , satisfying the relation |z +i|=|z+ 2| . Illustrate the locus of z in the Argand plane

Find the locus of a complex number z=x+ iy satisfying the relation |2z+3i|<=|2z+5|. Illustrate the locus in Argand plane.

Find the locus of a complex number z= x+ yi satisfying the relation arg (z-a)=(pi)/(4), a in R Illustrate the locus of z in the Argand plane

Find the locus of a complex number z such that arg ((z-2)/(z+2))= (pi)/(3)

The locus of a complex number z satisfying |z-(1+3i)|+|z+3-6i|=4

If n is a positive integer greater than unity z is a complex number satisfying the equation z^(n)=(z+1)^(n), then

If z is a complex number satisfying z + z^-1 = 1 then z^n + z^-n , n in N , has the value