[tex]i = \sqrt{-1} ~~~~~=\ \textgreater \ \;\;\;\;\; i^2=-1 \\ \\
( 1+zi)(3-5i) = \\
=3 \times 1 + 3 \times zi - 5i \times 1 -5i \times zi = \\
= 3 + 3zi-5i -5zi^2 = \\
= 3+ 3zi-5i - 5z \times (-1)= \\
=3+ 3zi-5i+5z =\boxed{(3+5z) + i(3z-5)}= \boxed{(3-5i) +z(5+3i)}[/tex]
