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)

if arg(z+a)=pi/6 and arg(z-a)=(2pi)/3 then

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

The area bounded by the curves x^2+y^2=1,x^2+y^2=4 and the pair of lines sqrt3 x^2+sqrt3 y^2=4xy , in the first quadrant is (1) pi/2 (2) pi/6 (3) pi/4 (4) pi/3

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

A point z moves in the Argand plane such that |z-3i|=2, then its locus is-

Let z in C and if A={z:"arg"(z)=pi/4} and B={z:"arg"(z-3-3i)=(2pi)/3} . Then n(A frown B)=

If z = x + iy and arg ((z-1)/(z+1))=(pi)/(4) , then the locus of (x, y) is

The area bounded by y=sec^-1 x,y=cosec^-1x, and line x-1=0 is (a) log(3+2sqrt2)-pi/2 sq. units (b) pi/2-log(3+2sqrt2) sq. units (c) pi-(log)_e 3 sq. units (d) non of these

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

If A(3/sqrt(2), sqrt(2)) , B(-3/sqrt(2), sqrt(2)), C(-3/sqrt(2), -sqrt(2)) and D(3 cos theta , 2 sin theta) are four points . If the area of the quadrilateral ABCD is maximum where theta in (3 pi/2, 2 pi) then (a) maximum area is 10 sq units (b) theta = 7 pi/4 (c) theta = 2 pi- sin^(-1) 3/ sqrt(85) (d) maximum area is 12 sq units