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:
$=\dfrac{1^2-2(1)(i) + i^2}{1^2-i^2}
\\=\dfrac{1-2i+i^2}{1-i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{1-2i+(-1)}{1-(-1)}
\\=\dfrac{-2i}{1+1}
\\=\dfrac{-2i}{2}
\\=-i$
