(1) Find the value of `(sqrt3/2+i/2)^5-(sqrt3/2-i/2)^5`

find the value of ( 3 + sqrt3 ) xx ( 2 + sqrt2 )

Show that (sqrt3/2 + i/2)^3 = i

Find the value of a and b if (i)(sqrt(3)+1)/(sqrt(3)-1)=a+bsqrt(3)" "(ii)(5+2sqrt(3))/(5-2sqrt(3))=a+bsqrt(3)

(i) If x = (6ab)/(a + b) , find the value of : (x + 3a)/(x - 3a) + (x + 3b)/(x - 3b) . (ii) a = (4sqrt(6))/(sqrt(2) + sqrt(3)) , find the value of : (a + 2sqrt(2))/(a - 2sqrt(2)) + (a + 2sqrt(3))/(a - 2sqrt(3)) .

If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/2)^5 , then prove that I m(z)=0.

If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(z)=0

[(sqrt(5)+i/2)(sqrt(5)-i2)]-:(6+i5)

Find the modulus and amplitude of (-1)/(2)+ (sqrt3)/(2)i

Find the value of the "determinant" |{:(sqrt13+sqrt3,2sqrt5,sqrt5),(sqrt26+sqrt15,5,sqrt10),(sqrt65+3,sqrt15,5):}|

Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[sqrt((15))+sqrt((26)),5,sqrt((10))],[3+sqrt((65)),sqrt((15)),5]|