[tex]\begin{gathered} \frac{z}{w}=\frac{2+3i}{5-4i}\times\frac{(5+4i)}{(5+4i)} \\ =\frac{10+8i+15i+12i^2}{25-16i^2} \\ =\frac{10+23i-12}{25+16} \\ =\frac{-2+23i}{41} \\ =\frac{-2+23i}{41} \\ \bar{(\frac{z}{w})}=\frac{-2-23i}{41} \end{gathered}[/tex][tex]\begin{gathered} \frac{\bar{z}}{\bar{w}}=\frac{2-3i}{5+4i} \\ =\frac{2-3i}{5+4i}\times\frac{5-4i}{5-4i} \\ =\frac{10-8i-15i+12i^2}{25-16i^2} \\ =\frac{10-23i-12}{25+16} \\ =\frac{-2-23i}{41} \end{gathered}[/tex]
Hence, it is shown that Left hand side is equal to right hand side.
