`" If "(4+sqrt(15))^(n)=I+F" when "I," n are positive integers,"0ltFlt1" then "(I+F)(1-F)`

If (5+2sqrt(6))^(n)=m+f, where n and m are positive integers and 0<=f<=1, then (1)/(1-f)-f is equal to

Show that (-sqrt(-1))^(4n+3) =i , where n is a positive integer.

((1+i)/(1-i))^(4n+1) where n is a positive integer.

If (6+sqrt(35))^(n)= I+F when I is odd and 0ltFlt1, then (1+F)(1-F)=

If (6+sqrt(35))^(n)=I+F when I is odd and 0ltFlt1 , then (I+F)(1-F)-1=

If (2+sqrt(3))^n=I+f, whare I and n are positive integers and 0

If n is a positive integer,then (1+i)^(n)+(1-1)^(n) is equal to

If (9 + 4 sqrt(5))^(n) = I + f ,n and l being positive integers and f is a proper fraction , show that (I-1 ) f + f^(2) is an even integer.

For a positive integer n, what is the value of i^(4n+1) ?