A) \[{{x}^{2}}+x+1=0\]
B) \[{{x}^{2}}-2x+2=0\]
C) \[{{x}^{2}}+2x+2=0\]
D) \[{{x}^{2}}+2x-2=0\]
Correct Answer: B
Solution :
Let \[x=1+i\Leftrightarrow x-1=i\] \[\Leftrightarrow {{(x-1)}^{2}}={{i}^{2}}\Leftrightarrow {{x}^{2}}-2x+1=-1\] \[\Leftrightarrow {{x}^{2}}-2x+2=0\].
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