Given complex numbers are,
[tex](-2+3i),(4-5i)[/tex]To find the product of the given complex numbers,
[tex]\begin{gathered} (-2i+3i)(4-5i)=-2i\times4+(-2i)(-5i)+3i\times4+3i(-5i) \\ \text{ =}-8i+10i^2+12i-15i^2 \end{gathered}[/tex]Now subsitute the value of ,
[tex]i^2=-1[/tex]So we get,
[tex]\begin{gathered} -8i+10i^2+12i-15i^2=-8i+10(-1)+12i-15(-1) \\ \text{ =-8i-10+12i+15} \end{gathered}[/tex]Now add the like terms,
[tex]-8i+12i+15-10=4i+5[/tex]So the required value is in the form,
[tex]a+ib=4i+5[/tex]