Answer
$i$
Work Step by Step
Multiply both the numerator and the denominator by the conjugate of the denominator, which is $1+i$, to obtain:
$=\dfrac{(1+i)(1+i)}{(1-i)(1+i)}$
Simplify using the rules $(a-b)(a+b)=a^2-b^2$ and $(a+b)(a+b)=a^2+2ab+b^2$ to obtain:
$=\dfrac{1^2+1(1)(i) + i^2}{1^2-i^2}
\\=\dfrac{1+2i+i^2}{1-i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{1+2i+(-1)}{1-(-1)}
\\=\dfrac{2i}{1+1}
\\=\dfrac{2i}{2}
\\=i$
