`lim_(z->-3)[sqrt(z+6)/z]`

(lim)_(z->1)(z^(1/3)-1)/(z^(1/6)-1)

z is such that a r g ((z-3sqrt(3))/(z+3sqrt(3)))=pi/3 then locus z is

If x=int_(0)^(t^(2))e^(sqrt(z)){(2tan sqrt(z)+1-tan^(2)sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz and y=int_(0)^(t^(2))e^(sqrt(z)){(1-tan^(2)sqrt(z)-2tan sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz : Then the inclination of the tangent to the curve at t=(pi)/(4) is :

Let z_1=6+i and z_2=4-3i . If z is a complex number such thar arg ((z-z_1)/(z_2-z))= pi/2 then (A) |z-(5-i)=sqrt(5) (B) |z-(5+i)=sqrt(5) (C) |z-(5-i)|=5 (D) |z-(5+i)|=5

For any two complex numbers, z_(1),z_(2) |1/2(z_(1)+z_(2))+sqrt(z_(1)z_(2))|+|1/2(z_(1)+z_(2))-sqrt(z_(1)z_(2))| is equal to

int(dz)/(z sqrt(z^(2)-1))

If log_(sqrt3) |(|z|^2 -|z| +1|)/(|z|+2)|<2 then locus of z is

If arg ((z-6-3i)/(z-3-6i))=pi/4 , then maximum value of |z| :

If |z_(1)|=|z_(2)|=|z_(3)|=1 and z_(1)+z_(2)+z_(3)=sqrt(2)+i , then the complex number z_(2)barz_(3)+z_(3)barz_(1)+z_(1)barz_(2) , is

Let z_1, z_2, z_3 be the three nonzero complex numbers such that z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot Let |a b c b c a c a b|=0 a r g(z_3)/(z_2)=a r g((z_3-z_1)/(z_2-z_1))^2 orthocentre of triangle formed by z_1, z_2, z_3, i sz_1+z_2+z_3 if triangle formed by z_1, z_2, z_3 is equilateral, then its area is (3sqrt(3))/2|z_1|^2 if triangle formed by z_1, z_2, z_3 is equilateral, then z_1+z_2+z_3=0