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

Locate the region in the Argand plane determined by z^2+ z ^2+2|z^2|<(8i( z -z)) .

|z-4|lt|z-2| represents the region given by

If the imaginary part of (2z + 1)/(iz + 1) is -2 , then show that the locus of the point representing z in the argand plane is straight line.

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

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

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

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

If z=omega,omega^2w h e r eomega is a non-real complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane, then the third vertex z may be represented by (a) z=1 b. z=0 c. z=-2 d. z=-1

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_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are