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Answer:
43-7i
Step-by-step explanation:
We are given the expression:
[tex] \displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}[/tex]
First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.
[tex] \displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)} \\ \displaystyle \large{[18i + 21 - 24 {i}^{2} - 28i]- (2 - 3i)} [/tex]
Now combine like terms.
[tex] \displaystyle \large{[ - 10i+ 21 - 24 {i}^{2} ]- (2 - 3i)} [/tex]
Imaginary Unit
[tex] \displaystyle \large{i = \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2} = - 1 } [/tex]
Therefore:-
[tex] \displaystyle \large{[ - 10i+ 21 - 24 ( - 1) ]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 21 + 24]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 45]- (2 - 3i)} [/tex]
Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.
[tex] \displaystyle \large{- 10i+ 45 - (2 - 3i)} \\ \displaystyle \large{- 10i+ 45 - 2 + 3i} [/tex]
Combine like terms.
[tex] \displaystyle \large{43 - 7i} [/tex]