Question

Let Z be a complex Numbers satisfying the equation $z^2$ - (11 + i) z+k+3i = 0 where k $ϵ$ R and i = $\sqrt{(-i)}$, suppose equation has one real and one non-real root. Find the non-real root.

• A. 7 + i
• B. 5 + i
• C. 8 + i
• D. 4 + i

Answer 1

The correct option is C

8 + i

Let $\alpha$ be the real root $\alpha$ should satisfy the equation.

Substitute $\alpha$ in place of z in the above given equation.

${\alpha }^2$ - (11+i) $\alpha$ + k + 3i = 0

$({\alpha }^2$ - 11$\alpha$ + k) + i( 3 - $\alpha$) = 0

Comparing the real and imaginary part on both side

${\alpha }^2$ - 11α + k = 0

3 - $\alpha$ = 0

$\alpha$ = 3

Let the non-real root be β

Sum of the root $\alpha$ + β = $\frac{(-b)}{a}$

3 + β = 11 + i

β = 8 + i

Non real root = 8 + i