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