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(3-4i)(6i+7)-(2-3i)

i need all the work laid out :P pls help this test was due last week!
also the answer is 43 - 7i but i need the work <3

Sagot :

VectorFundament120

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]

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