3+sqrt(3))(3*sqrt(3))

If (3+2sqrt(3))/(3-sqrt(3))=a+sqrt(3)b , then the value of sqrt(a+b) , where a and b are rational numbers, is

((3+i sqrt(3))(3-i sqrt(3)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-i sqrt(2)))

z is such that arg((z-3sqrt(3))/(z+3sqrt(3)))=(pi)/(3) then locus z is

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

No tangent can be drawn from the point ((5)/(2),1) to the circumcircle of the triangle with vertices (1,sqrt(3)),(1,-sqrt(3)),(3,-sqrt(3))

No tangent can be drawn from the point (5/2,1) to the circumcircle of the triangle with vertices (1,sqrt(3)),(1,-sqrt(3)),(3,-sqrt(3)) .

If A=log_(sqrt(3))(sqrt(3sqrt(3sqrt(3sqrt(3)))))* then the value of log_(sqrt(2))(8A+1) is equal to

Show that the points (-3, -3), (3, 3) and (-3sqrt(3), 3sqrt(3)) are the vertices of an equilateral triangle.

The values of parameter a for which the point of minimum of the function f(x)=1+a^(2)x-x^(3) satisfies the inequality (x^(2)+x+2)/(x^(2)+5x+6)<0 are (2sqrt(3),3sqrt(3))(b)-3sqrt(3),-2sqrt(3))(-2sqrt(3),3sqrt(3))(d)(-2sqrt(2),2sqrt(3))

Find the area and nature of the triangle formed by the points represented by the complex numbers (3+3i),(-3-3i) and (-3sqrt(3)+3sqrt(3)i) .