Given that the two curves `a r g(z)=pi/6 and |z-2sqrt(3)i|=r` intersect in two distinct points, then a. `[r]!=2` b. `0 < r < 3` c. `r=6` d. `3 < r < 2sqrt(3)` (Note : [r] represents integral part of r)

If two circles (x-1)^2+(y-3)^2=r^2 and x^2+y^2-8x+2y+8=0 intersect in two distinct points then

If two circles (x-1) ^(2) + (y-3) ^(2) =r^(2)and x ^(2) +y^(2) -8x +2y + 8=0 intersect in two distinct points, then-

Find the point of intersection of the curves a r g(z-3i)=(3pi)/4 and arg(2z+1-2i)=pi//4.

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

Given that Delta = 6,r_1=2, r_(2) = 3, r_(3) = 6 then Inradius is equal to

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

Identify the locus of z if bar z = bar a +(r^2)/(z-a).

Prove that the domain of g(x) = cot^-1 x/sqrt(x^2 - [x]) , x in R is R - { sqrtn : n ge 0 , n in z} .

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

z_1, z_2 and z_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1 and kz_3 are in G.P. where k in R^+dot