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

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

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

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

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

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

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

Show that (frac{1+i}{sqrt 2})^8 + (frac{1-i}{sqrt 2})^8 = 2

Solve the following: If a = (-1 + sqrt(3)i) / 2 , b = (-1 - sqrt(3)i) / 2 , show that a^2 = b and b ^2 = a