`((1+i)/(sqrt(2)))^8+((1-i)/(sqrt(2)))^8` is equal to

1+(sqrt(2))/(2-sqrt(2)) is equal to

Show that ((-1+sqrt(3)i)/2)^n+((-1-sqrt(3i))/2)^n is equal to 2 when n is a multiple of 3 and is equal to -1 when n is any other positive integer.

If sqrt(2)=1. 4142 , then sqrt((sqrt(2)-1)/(sqrt(2)+1)) is equal to

1/(sqrt(9)-\ sqrt(8)) is equal?

Prove that : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqrt(2)) (iii) sqrt(i)+sqrt(-i)=sqrt(2)

Lt_(x to 0)(cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+4)-2) is equal to (i) 4 (ii) -4 (iii) 8 (iv) -8

The value of |-1 2 1 3+2sqrt(2) 2+2sqrt(2) 1 3-2sqrt(2) 2-2sqrt(2) 1| is equal to a. zero b. -16sqrt(2) c. -8sqrt(2) d. none of these

("lim")_(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))i se q u a lto 1/2 (b) 2 (c) 1 (d) none of these

Rationalise the denominator of each the following (i)(2)/(sqrt(3))" "(ii)(1)/(3sqrt(5))" "(iii)(1)/(sqrt(8))" "(iv)(sqrt(2)+1)/(sqrt(3))

lim_(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to