" 3."quad n in N,((1+i)/(sqrt(2)))^(8n)+((1-i)/(sqrt(2)))^(8n)=

If n in N((1+i)/(sqrt(2)))^(8n)+((1-i)/(sqrt(2)))^(8)n is

((-1+i sqrt(3))/(2))^(3 n)+((-1-i sqrt(3))/(2))^(3 n)=

If i^(2)=-1 and ((1+i)/(sqrt2))^(n)=((1-i)/(sqrt2))^(m)=1, AA n, m in N , then the minimum value of n+m is equal to

Show that the integral part in each of the following is odd. n in N . (i) (5+2sqrt(6))^(n) (ii) (8+3 sqrt(7))^(n) (iii) (6+sqrt(35))^(n)

When n=8,(sqrt(3)+i)^(n)+(sqrt(3)-i)^(n)=

What is the value of ((-1+i sqrt(3))/(2))^(3n)+((-1-i sqrt(3))/(2))^(3n), where i=sqrt(-1)?

{:(" "Lt),(n rarr oo):} ((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+(1)/(sqrt(n^(2)+3n))+....(1)/(sqrt(n^(2)+n(n-1)))))=

the value of ((-1+sqrt(3)i)/(2))^(3n)+((-1-sqrt(3)i)/(2))^(3n)=

n is any integer then arg(((sqrt(3)+i)^(4n+1))/((1-sqrt(3)i)^(4n)))=....

If n is a positive integer, which of the following two will always be integers: (I) (sqrt(2)+1)^(2n)+(sqrt(2)-1)^(2n) (II) (sqrt(2)+1)^(2n)-(sqrt(2)-1)^(2n) (III) (sqrt(2)+1)^(2n+1)+(sqrt(2)-1)^(2n+1) (IV) (sqrt(2)+1)^(2n+1)-(sqrt(2)-1)^(2n+1)