Answer: The required product is [tex]-11+62i.[/tex]
Step-by-step explanation: We are given to find the product of the following two complex numbers :
[tex]z_1=6+5i,~~~z_2=4+7i.[/tex]
We will be using the following property :
[tex](a+b)(c+d)=a(c+d)+b(c+d).[/tex]
Also, we will use the fact that [tex]i=\sqrt{-1},~~i^2=-1.[/tex]
The product of the given complex numbers is
[tex]z_1z_2\\\\=(6+5i)(4+7i)\\\\=6(4+7i)+5i(4+7i)\\\\=24+42i+20i+35i^2\\\\=24+62i-35\\\\=-11+62i.[/tex]
Thus, the required product is [tex]-11+62i.[/tex]
