Question

For a complex number $z$ , the product of the real parts of the roots of the equation $z^{2}-z=5-5i$ is (where, $i=\sqrt{- 1}$ )

• A. $-25$
• B. $-6$
• C. $-5$
• D. 25

Answer 1

Answer: (B)

Equation is $z^{2}-z-5+5i=0$
$\Rightarrow z=\frac{1 \pm \sqrt{1 + 20 - 20 i}}{2}$
$\Rightarrow z=\frac{1 \pm \sqrt{\left(5 - 2 i\right)^{2}}}{2}$
$\Rightarrow z=\frac{1 \pm \left(5 - 2 i\right)}{2}=3-i,-2+i$
The required value $=-6$