" Let "n in" Nanda "=sqrt(sin((pi)/(n)))i-sqrt(cos((pi)/(n)))j" .If "|a|=(1)/(2)sqrt(n)," then "n" is "

Let n be a positive integer such that sin((pi)/(2^(n)))+cos((pi)/(2^(n)))=(sqrt(n))/(2), then

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

sum_(n=1)^(20)[sin((2n pi)/(21))-i cos((2n pi)/(21))]=

Let n be a positive integer such that sin(pi/(2n))+cos(pi/(2n))=(sqrt(n))/2dot Then

Let n be a positive integer such that sin(pi/(2n))+cos(pi/(2n))=(sqrt(n))/2 Then

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

Let n be a positive integer such that sin (pi/(2n))+cos(pi/(2n))=(sqrt(n))/2dot Then

If the sum of (n-1) terms of the series sin((pi)/(n))+sin((2 pi)/(n))+sin((3 pi)/(n))+.... is equal to 2+sqrt(3), then find the value of n.

(i) ((root(n)(a))^(sqrt(n)))^(sqrt(n))