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Sagot :

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]

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