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maks197457 [2]
2 years ago
8

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

Mathematics
1 answer:
Sergeu [11.5K]2 years ago
5 0

Answer:

43-7i

Step-by-step explanation:

We are given the expression:

\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}

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.

\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)}

Now combine like terms.

\displaystyle \large{[ - 10i+ 21  - 24 {i}^{2} ]- (2 - 3i)}

<u>I</u><u>m</u><u>a</u><u>g</u><u>i</u><u>n</u><u>a</u><u>r</u><u>y</u><u> </u><u>U</u><u>n</u><u>i</u><u>t</u>

\displaystyle \large{i =   \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2}  =   - 1 }

Therefore:-

\displaystyle \large{[ - 10i+ 21  - 24  ( - 1) ]- (2 - 3i)}  \\   \displaystyle \large{[ - 10i+ 21   + 24]- (2 - 3i)}  \\   \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}

Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.

\displaystyle \large{- 10i+ 45 -  (2 - 3i)}  \\   \displaystyle \large{- 10i+ 45 -  2 + 3i}

Combine like terms.

\displaystyle \large{43 - 7i}

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