Question

Write the conjugate of complex number $\frac{5i}{7+i}$

Answer 1

$\frac{5i}{7+i}\cdot \frac{7-i}{7-i}$, rationalize the denominator

$=\frac{5i(7-i)}{7^2-i^2}=\frac{35i-5i^2}{49+1}$

$=\frac{35i+5}{50}=\frac{1}{10}+\frac{7}{10}i$

Hence conjugate is $\frac{1}{10}-\frac{7}{10}i$

Note: Conjugate of $x+iy$ is $x-iy$