Answer
Answer: A
Work Step by Step
$ x^{2}-4x+4=-1\qquad$ ...write left side as a binomial squared.($(a\pm b)^{2}=a^{2}\pm 2ab+b^{2}$)
$a=x,b=2$
$(x-2)^{2}=-1\qquad$ ...take square roots of each side.
$ x-2=\pm\sqrt{-1}\qquad$ ...simplify.($\sqrt{-1}=i$)
$ x-2=\pm i\qquad$ ...add $2$ to each side.
$ x-2+2=\pm i+2\qquad$ ...simplify.
$x=2\pm i$
