Find the conjugate of $\frac{5 i}{7+i}$
Find the conjugate of $\frac{5 i}{7+i}$
- $\frac{1}{10}(1-7 i)$
- $\frac{1}{10}(7 i-1)$
- $\frac{1}{10}(1+7 i)$
- $\frac{1}{\sqrt{50}}(1-7 i)$
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
Asked in: AP EAMCET 2020 (22 Sep Shift 2)
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