Find the conjugate of frac{5i}{7+i}. | vedclass

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Question

(A) To find the conjugate of $z = \frac{5i}{7+i}$,we first simplify the expression by multiplying the numerator and denominator by the conjugate of th

Vedclass · Accepted Answer

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

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(A) To find the conjugate of $z = \frac{5i}{7+i}$,we first simplify the expression by multiplying the numerator and denominator by the conjugate of the denominator,which is $(7-i)$.$z = \frac{5i}{7+i} 	imes \frac{7-i}{7-i}$$z = \frac{35i - 5i^2}{7^2 - i^2}$Since $i^2 = -1$,we have:$z = \frac{35i - 5(-1)}{49 - (-1)} = \frac{5 + 35i}{50}$Dividing both terms by $5$,we get:$z = \frac{1 + 7i}{10} = \frac{1}{10} + \frac{7}{10}i$The conjugate of a complex number $a + bi$ is $a - bi$.Therefore,the conjugate of $\frac{1}{10} + \frac{7}{10}i$ is $\frac{1}{10} - \frac{7}{10}i = \frac{1}{10}(1-7i)$.Thus,option $A$ is correct.

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

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