KEAM 2011 Math Paper

Equation, x2−x+(1−i)=0 and one root is given, say α=1+i and second root is β.
since, the given root in complex form so, the other root is also complex form.
Sum of the roots =α+β=−(−1)
β=1−α=1−(1+i)=−i
∴ The other root is −i