Question

If $(1 + i)$ is a root of the equation $x^{2} - x + (1 - i) = 0$, then the other root is

• A. $1-i$
• B. $i$
• C. $-i$
• D. $2i$
• E. $-2i$

Answer 1

Answer: (C)

Equation, $x^{2}-x+(1-i)=0$
and one root is given, say $\alpha=1+i$ and second root is $\beta$
Since, the given root in complex form so, the other root is also complex form.
Sum of the roots $=\alpha+\beta=-(-1)$
$\beta=1-\alpha=1-(1+i)=-i$
$\therefore $ The other root is $-i$