The set of points on the complex plane such that `z^2 + z+ 1` is real and positive (where `z = x +i y, x, y in R`) is

Find the set of points on the argand plane for which the real part of the complex number (1 + i)z^2 is positive where z = x + iy, x , y in R and i = sqrt(-1 ) .

The set of points z in the complex plane satisfying |z-i|z||=|z+i|z|| is contained or equal to the set of points z satisfying

The set of points z in the complex plane satisfying |z-i|z||=|z+i|z|| is contained or equal to the set of points z satisfying

If alpha be the real cube root of and beta,gamma be the complex cube roots of m, a real positive number,then for any x,y,z show that (x beta+y gamma+z alpha)/(x gamma+y alpha+z beta)=omega^(2), where omega is a complex cube root of unity.

If z = x + i y and . P represents z in the Argands plane. Find the locus of P when: The real part of (z + 1) / (z + i) is 1

The point of interesection of the line x = y = z with the plane x + 2y + 3z = 6 is (1,1,-1).

If x, y, z are positive real numbers such that x+y+z=a, then

If x, y, z are positive real numbers such that x+y+z=a, then

Let x_1 and y_1 be real numbers. If z_1 and z_2 are complex numbers such that |z_1| = |z_2|=4 , then |x_1 z_1 - y_1 z_2|^(2) + |y_1 z_1 + x_1 z_2 |^(2) is equal to