Find the conjugate of the complex number (1+i)^2n+1 / (1-i)^2n-1 , n is natural no.

(1+i)/(1-i)   = (1+i)² /[(1+i)*(1-i)]   = 2i /2 =i
(1+i)²ⁿ⁺¹ /(1-i)^2n-1   = [(1+i)/(1-i)]²ⁿ *[(1+i)*(1-i)] = i²ⁿ * 2 = 2[(i)²]ⁿ= 2*(-1)ⁿ
so, it is purely real, its conjugate is the number itself.
hope you understood