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