If `(log)_(sqrt(3))((|z|^2-|z|+1)/(2+|z|))>2,` then locate the region in the Argand plane which represents `zdot`

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

A point z moves in the Argand plane such that |z-3i|=2, then its locus is-

If z=x+iy and |z-3|/|z+3|=2, find the position of the point z in the Argand diagram.

If z is a complex number such taht z^2=( barz)^2, then find the location of z on the Argand plane.

Let z=1-t+isqrt(t^2+t+2) , where t is real parameter. The locus of z in the argand plane is

Let A(z_1),B(z_2) and C(z_3) be the three points in Argands plane The point A B and C are collinear if

If z_(1)andz_(2) be two non-zero complex numbers such that (z_(1))/(z_(2))+(z_(2))/(z_(1))=1 , then the origin and the points represented by z_(1)andz_(2)

Given that the complex numbers which satisfy the equation | z bar z ^3|+| bar z z^3|=350 form a rectangle in the Argand plane with the length of its diagonal having an integral number of units, then area of rectangle is 48 sq. units if z_1, z_2, z_3, z_4 are vertices of rectangle, then z_1+z_2+z_3+z_4=0 rectangle is symmetrical about the real axis a r g(z_1-z_3)=pi/4or(3pi)/4

Plot the region represented by pi/3lt=a r g((z+1)/(z-1))lt=(2pi)/3 in the Argand plane.

Let z_1 be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and z_1 ne+-1 consider an equilateral triangle inscribed in the circle with z_1,z_2,z_3 as the vertices taken in the counter clockwise directtion then z_1z_2z_3 is equal to