The conjugate of the complex number frac{2 + | vedclass

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Question

(B) Let $z = \frac{2 + 5i}{4 - 3i}$.To simplify,multiply the numerator and denominator by the conjugate of the denominator,$4 + 3i$:$z = \frac{(2 + 5i

Vedclass · Accepted Answer

$\frac{-7 - 26i}{25}$

Vedclass · Answer

(B) Let $z = \frac{2 + 5i}{4 - 3i}$.To simplify,multiply the numerator and denominator by the conjugate of the denominator,$4 + 3i$:$z = \frac{(2 + 5i)(4 + 3i)}{(4 - 3i)(4 + 3i)}$$z = \frac{8 + 6i + 20i + 15i^2}{16 + 9}$Since $i^2 = -1$,we have:$z = \frac{8 + 26i - 15}{25} = \frac{-7 + 26i}{25}$The conjugate of $z = a + bi$ is $\bar{z} = a - bi$.Therefore,the conjugate of $\frac{-7 + 26i}{25}$ is $\frac{-7 - 26i}{25}$.

The conjugate of the complex number $\frac{2 + 5i}{4 - 3i}$ is

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