Consider curves `C_(1):|arg (z-2)|=(pi)/(4) ; C_(2):|arg(z+2)|=(3 pi)/(4)` and `C_(3):|z-alpha i|=4sqrt(2),alpha inR` on the complex plane such that `C_(3)` touches both `C_(1)` and `C_(2)` . Then the sum of absolute value(s) of `alpha` is equal to

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

Find the complex number z if arg (z+1)=(pi)/(6) and arg(z-1)=(2 pi)/(3)

Area bounded by arg (z)=(pi)/(3), Arg (z)=(2 pi)/(3) and Arg(z-2-i2sqrt(3))=pi in the complex plane is (in square unit) 2sqrt(3)(b)4sqrt(3)(c)sqrt(3) (d) None of these

Let A(z_(1)) be the point of intersection of curves arg(z-2+i)=(3 pi)/(4)) and arg(z+i sqrt(3))=(pi)/(3),B(z_(2)) be the point on the curve ar g(z+i sqrt(3))=(pi)/(3) such that |z_(2)-5|=3 is minimum and C(z_(2)) be the centre of circle |z-5|=3. The area of triangle ABC is equal to

Two circles in the complex plane are {:(C_(1) : |z-i|=2),(C_(2) : |z-1-2i|=4):} then

If arg(z+a)=pi/6 " and " arg(z-a)=(2pi)/(3)(a in R^(+)) , then

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

Number of z, which satisfy Arg(z-3-2i)=(pi)/(6) and Arg(z-3-4i)=(2 pi)/(3) is/are :

If z_(1) and z_(2) are two non-zero complex number such that |z_(1)z_(2)|=2 and arg(z_(1))-arg(z_(2))=(pi)/(2) ,then the value of 3iz_(1)z_(2)

If pi/5 and pi/3 are the arguments of bar(z)_(1) and bar(z)_(2), then the value of arg(z_(1))+arg(z_(2)) is