ExamBro
ExamBro
AP EAMCET · Maths · Complex Number

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

  1. A \(\frac{1}{10}(1-7 i)\)
  2. B \(\frac{1}{10}(7 i-1)\)
  3. C \(\frac{1}{10}(1+7 i)\)
  4. D \(\frac{1}{\sqrt{50}}(1-7 i)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{10}(1-7 i)\)

Step-by-step Solution

Detailed explanation

\(\frac{5 i}{7+i}=\frac{5 i}{7+i} \times \frac{7-i}{7-i}\) \[ \begin{aligned} & =\frac{5 i(7-i)}{(7)^2-(i)^2}=\frac{5\left(7 i-i^2\right)}{50} \quad\left\{\because i^2=-1\right\} \\ \frac{5 i}{7+i} & =\frac{1+7 i}{10} \end{aligned} \] \(\therefore\) Conjugate of…