Given that the two curves `a r g(z)=pi/6a n d|z-2sqrt(3)i|=r` intersect in two distinct points, then

If the two circles (x+1)^2+(y-3)=r^2 and x^2+y^2-8x+2y+8=0 intersect in two distinct point,then (A) r > 2 (B) 2 < r < 8 (C) r < 2 (D) r=2

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then -1 1 m in R (d) none of these

Let l_(1) and l_(2) be the two skew lines. If P, Q are two distinct points on l_(1) and R, S are two distinct points on l_(2) , then prove that PR cannot be parallel to QS.

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)

Show that the lines (x-3)/(3)=(y-3)/(-1),z-1=0and(x-6)/(2)=(z-1)/(3),y-2=0 intersect. Also find the point of intersection.'

A particle P starts from the point z_0=1+2i , where i=sqrt(-1) . It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z_1dot From z_1 the particle moves sqrt(2) units in the direction of the vector hat i+ hat j and then it moves through an angle pi/2 in anticlockwise direction on a circle with centre at origin, to reach a point z_2dot The point z_2 is given by (a) 6+7i (b) -7+6i (c) 7+6i (d) -6+7i

Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)

z_1, z_2a n dz_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1a n d kz_3 are in G.P. where k in R^+dot

Consider the curves y^(2) = x and x^(2) = y . (i) Find the points of intersection of these two curves. (ii) Find the area between these two curves.