`frac{sqrt3 +i}{ -1-i sqrt(3)}` = ?

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

If in a "Delta"A B C ,\ A=(0,0),\ B=(3,3sqrt(3)), C-=(-3sqrt(3),3) then the vector of magnitude 2sqrt(2) units directed along A O ,\ w h e r e\ O is the circumcentre of A B C is a. (1-sqrt(3)) hat i+(1+sqrt(3)) hat j b. (1+sqrt(3)) hat i+(1-sqrt(3)) hat j c. (1+sqrt(3)) hat i+(sqrt(3)-1) hat j d. none of these

The area of the triangle formed by three point sqrt3 +i, -1+sqrt3i and (sqrt3-1) +(sqrt3+1)i is ________

If 3^(49)(x+i y)=(3/2+(sqrt(3))/2i)^(100) and x=k y then k is: a. -1//3 b. sqrt(3) c. -sqrt(3) d. -1/(sqrt(3))

Express the following in the form a+bi (sqrt3 + 5i) (sqrt3 -5i)^(2) + (-4+ 5i)^(2)

If z = (sqrt(3+i))/2 (where i = sqrt(-1) ) then (z^101 + i^103)^105 is equal to

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Calculate the modulus and argument of (w)/(z)

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Represent z and w accurately on the complex plane.

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Calculate the modulus and argument of w and z

Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1 ) Prove that each of these complex numbers is the square of the other