Show that `sqrt([-1sqrt({-1-sqrt(-1+ ..."to"oo)})]) = omega, or omega^(2)`

sqrt(-1-sqrt(-1-sqrt(-1oo))) is equal to (where omega is the imaginary cube root of unity and i=sqrt(-1))

Given that 1, omega, omega^(2) are cube roots of unity. Show that (1- omega + omega^(2))^(5) + (1 + omega - omega^(2))^(5)= 32

sqrt 2(sqrt 2+1) - sqrt 2 (1+sqrt2) =?

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)=5

lim_(x rarr oo)(sqrt(x+1)-sqrt(x))

lim_(n rarr oo)n[sqrt(n+1)-sqrt(n))]

If y=sqrt(x+sqrt(x+sqrt(x+\ dotto\ oo))) , prove that (dy)/(dx)=1/(2\ y-1)

lim_(h rarr oo)log(sqrt(h-1)+sqrt(h))

Let omega be a complex number such that 2omega+1=z where z=sqrt(-3.) If|1 1 1 1-omega^2-1omega^2 1omega^2omega^7|=3k , then k is equal to : -1 (2) 1 (3) -z (4) z