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

(-i)^(4n+3), where n Is a positive integer.

If I_(n)=int_(0)^((pi)/(4))tan^(n)xdx, where n is a positive integer,then I_(10)+I_(8) is equal to (A)(1)/(9)(B)(1)/(8) (C) (1)/(7)(D)9

Find the value of (-1)^(n)+(-1)^(2n)+(-1)^(2n_1)+(-1)^(4n+2) , where n is any positive and integer.

Solve (x-1)^(n)=x^(n), where n is a positive integer.

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

Prove that (a)(1+i)^(n)+(1-i)^(n)=2^((n+2)/(2))*cos((n pi)/(4)) where n is a positive integer. (b) (1+i sqrt(3))^(n)+(1-i sqrt(3)^(n)=2^(n+1)cos((n pi)/(3)), where n is a positive integer

Prove that 2^(n)>1+n sqrt(2^(n-1)),AA n>2 where n is a positive integer.

The sum of the digits in (10^(2n^(2)+5n+1)+1)^(2) (where n is a positive integer),is

If ((1+i)/(1-i))^x=1 then (A) x=2n+1 , where n is any positive ineger (B) x=4n , where n is any positive integer (C) x=2n where n is any positive integer (D) x=4n+1 where n is any positive integer

The least positive value of n forwhich [(i(i+sqrt(3)))/(1-i^(2))]^(n) is a positive integer is