Q97 / 160 · AP EAMCET 2020 (22 Sep Shift 2) · Mathematics

Find the conjugate of $\frac{5 i}{7+i}$

  • Correct answer
    A
    $\frac{1}{10}(1-7 i)$
  • B
    $\frac{1}{10}(7 i-1)$
  • C
    $\frac{1}{10}(1+7 i)$
  • D
    $\frac{1}{\sqrt{50}}(1-7 i)$

Solution

$\frac{5 i}{7+i}=\frac{5 i}{7+i} \times \frac{7-i}{7-i}$ $$ \begin{aligned} & =\frac{5 i(7-i)}{(7)^2-(i)^2}=\frac{5\left(7 i-i^2\right)}{50} \quad\left\{\because i^2=-1\right\} \\ \frac{5 i}{7+i} & =\frac{1+7 i}{10} \end{aligned} $$ $\therefore$ Conjugate of $\frac{5 i}{7+i}$ is $\frac{1-7 i}{10}$ Hence, option (1) is correct.

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

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