Show that `((1)/( sqrt2) + (i)/( sqrt2 )) ^( 10) + ((1)/( sqrt2 ) - (i)/( sqrt2 )) ^( 10 ) = 0`

Show that (1 / sqrt(2) + i / sqrt(2))^10 + (1 / sqrt(2) - i / sqrt(2))^10 = 0 .

Show that ((1 + i ) /( sqrt2 )) ^( 8) + ((1 - i )/( sqrt2 )) ^( 8) = 2.

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

If U= [((1)/(sqrt2),(-1)/(sqrt2)),((1)/(sqrt2),(1)/(sqrt2))] , then U^(-1) is ....a) U^(T) b) U c) I d) O

Show that 4sqrt(2) I an irrational number.

If sin alpha = (-3)/(5), where pi lt alpha lt (3pi)/(2), then cos ((alpha)/(2))= ................ A) (-1)/( sqrt10) B) (1)/(sqrt10) C) (3)/(sqrt10) D) (-3)/(sqrt10)

Show that (frac{1}{sqrt 2}+frac{1}{sqrt 2}i )^10 + (frac{1}{sqrt 2}-frac{1}{sqrt 2}i )^10 = 0

Expand: (i) (sqrt 3 + sqrt 2)^4 (ii) (sqrt 5 - sqrt 2)^5

The value of cos 105^(@) is ............. A) (sqrt3+1)/(2sqrt2) B) (sqrt3-1)/(2sqrt2) C) -(sqrt3+1)/(2sqrt2) D) (1- sqrt3)/(2sqrt2)

Which term of G.P. sqrt(2) , 1/sqrt(2) , 1/(2sqrt(2)) , ….. is 1/(512sqrt(2)) ?