<PRE><B>Question 203100</B>
{{{x^2-2x+12}}} Start with the given expression.



{{{(1-2i)^2-2(1-2i)+12}}} Plug in {{{x=1-2i}}}



{{{1-4i+4i^2-2(1-2i)+12}}} FOIL



{{{1-4i+4i^2-2+4i+12}}} Distribute



{{{11+4i^2}}} Combine like terms.



{{{11+4(-1)}}} Plug in {{{i^2=-1}}}



{{{11-4}}} Multiply



{{{7}}} Subtract



So {{{(1-2i)^2-2(1-2i)+12=7}}} 



This means that {{{x^2-2x+12=7}}} when {{{x=1-2i}}}</PRE>