Intermediate Algebra for College Students (7th Edition)

$i$
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: $=\dfrac{1+2i+(-1)}{1-(-1)} \\=\dfrac{2i}{1+1} \\=\dfrac{2i}{2} \\=i$