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

What is the region represented by the inequality 3 lt |z-2-3i| lt 4 in the Argand plane

Find the center of the are represented by a r g[(z-3i)//(z-2i+4)]=pi//4 .

The area bounded by the curves arg z = pi/3 and arg z = 2 pi /3 and arg(z-2-2isqrt3) = pi in the argand plane is (in sq. units)

, a point 'z' is equidistant from three distinct points z_(1),z_(2) and z_(3) in the Argand plane. If z,z_(1) and z_(2) are collinear, then arg (z(z_(3)-z_(1))/(z_(3)-z_(2))). Will be (z_(1),z_(2),z_(3)) are in anticlockwise sense).

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

Given z_(1)=1 + 2i . Determine the region in the complex plane represented by 1 lt |z-z_(1)| le 3 . Represent it with the help of an Argand diagram

Prove that |Z-Z_1|^2+|Z-Z_2|^2=a will represent a real circle [with center (|Z_1+Z_2|^//2+) ] on the Argand plane if 2ageq|Z_1-Z_1|^2

Prove that |Z-Z_1|^2+|Z-Z_2|^2=a will represent a real circle [with center (|Z_1+Z_2|^//2+) ] on the Argand plane if 2ageq|Z_1-Z_1|^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

Find the area bounded by |arg z|lt=pi//4 and |z-1|<|z-3|dot