Given:
[tex](3-4i)(6i+7)-(2-3i)[/tex]
1. Arrange the expression, with the variables are written first
[tex](-4i+3)(6i+7)-(-3i+2)[/tex]
2. Distribute the "minus" operation
[tex](-4i+3)(6i+7)+3i-2[/tex]
3. Expand by multiplying the first two expressions
[tex](-4i+3)(6i+7)[/tex]
*multiply the first terms
[tex](-4i)(6i)=-24i^2[/tex]
*multiply the outer terms
[tex](-4i)(7)=-28i[/tex]
*multiply the inner terms
[tex](3)(6i)=18i[/tex]
*multiply the last terms
[tex](3)(7)=21[/tex]
This will give us:
[tex](-24i^2-28i+18i+21)[/tex]
*combine like terms
[tex](-24i^2-10i+21)+3i-2[/tex]
*Remove the parenthesis
[tex]-24i^2-10i+21+3i-2[/tex]
4. Combine like terms
[tex]-24i^2-7i+19[/tex]
The final answer would be:
[tex]-24i^2-7i+19[/tex]
