I am trying to solve the expression $$((i*(1+i))^n/((1-i)^{n-1}))$$ to the form A+iB. The answer given to this problem is $4*(-1)^{n+1} $, which is purely real. How much ever I try, couldn't get to this value, I give below my steps.
separating out , I get the expression$ = (i^n)*(1+i)*((1+i)/(1-i))^{n-1}.$
now $(1+i)/(1-i) = i. $
so the expression reduces to $$(i^n)*(1+i)*(i^{n-1}) = i^{2n-1}*(1+i)=(i^{2n})/(i))*(1+i)$$
now since $i^{2n} = (i^2)^n = (-1)^n$
so the expression $= (-1)^n*((1+i)/i) = ((-1)^n)*(1-i).$
This is the farthest I can get to, no way near $4*(-1)^{n+1}$.
Can someone help ? or is the answer incorrect?