Explanation
We must compute the product of two complex numbers:
[tex](6-7i)\times(4+6i).[/tex]
1) We apply the distributive property for the multiplication:
[tex]6\times4+6\times6i-7i\times4-7i\times6i.[/tex]
2) Simplifying the expression above, we have:
[tex]\begin{gathered} 24-42\times i^2+36i-28i, \\ =24-42\times(-1)+8i, \\ =66+8i. \end{gathered}[/tex]
Where we have used that the square of the imaginary unit is -1:
[tex]i^2=-1.[/tex]Answer
The result of the product is:
[tex]66+8i[/tex]
