Q4 / 108 · NTA Abhyas (JEE Main) 2020 · Mathematics · Complex Number

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

A
$- 25$
Correct answer
B
$- 6$
C
$- 5$
D
25

Solution

Equation is

z^{2} - z - 5 + 5 i = 0

\Rightarrow z = \frac{1 \pm \sqrt{1 + 20 - 20 i}}{2}

\Rightarrow z = \frac{1 \pm \sqrt{{(5 - 2 i)}^{2}}}{2}

\Rightarrow z = \frac{1 \pm (5 - 2 i)}{2} = 3 - i, - 2 + i

The required value

= - 6

Hence, the correct answer is option: 'B'.

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