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

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

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

Simiplify : ((1+i)/(1-i))^(4n+1) (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

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

Find the value of (-1)^(n)+(-1)^(2n)+(-1)^(2n_1)+(-1)^(4n+2) , where n is any positive and 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 (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4) , where n is a positive integer.

Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4) , where n is a positive integer.