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

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

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

((1+i)/(1-i))^(4n+1) 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.

Show that 7^(n) +5 is divisible by 6, where n is a positive integer

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

If A=[(3,-4),(1,-1)] , then prove that A^(n)=[(1+2n,-4n),(n,1-2n)] , where n is any positive integer.

If A,=[[3,-41,1]], then prove that A^(n),=[[1+2n,-4n][2n], where n is any positive integer.