Find the real and imaginary parts of the complex number $\dfrac{2 + 5i}{4 - 3i}$
The given complex number is
$\begin{aligned}
z & = \dfrac{2 + 5i}{4 - 3i} \\\\
& = \left(\dfrac{2 + 5i}{4 - 3i}\right) \times \left(\dfrac{4 + 3i}{4 + 3i}\right) \\\\
& = \dfrac{8 + 26 i + 15 i^2}{16 - 9 i^2} \\\\
& = \dfrac{-7 + 26 i}{25} \;\;\; \left[\because i^2 = -1\right] \\\\
& = \dfrac{-7}{25} + \dfrac{26i}{25}
\end{aligned}$
$\therefore$ $\;$ Real part $= \dfrac{-7}{25}$; $\;\;$ Imaginary part $= \dfrac{26}{25}$