Answer:
-10i + 45
Explanation:
To simplify the expression (3 - 4i)(6i + 7) - (2 - 3i), we can use the distributive property and combine like terms. Here are the steps:
1. Start by multiplying the two complex numbers (3 - 4i) and (6i + 7):
- (3 - 4i)(6i + 7) = 3 * 6i + 3 * 7 - 4i * 6i - 4i * 7
2. Simplify each term:
- 18i + 21 - 24i^2 - 28i
3. Simplify the imaginary unit squared:
- Remember that i^2 is equal to -1, so we can substitute it in the expression:
18i + 21 - 24(-1) - 28i
4. Simplify the expression further:
- Multiply -24 by -1:
18i + 21 + 24 - 28i
5. Combine like terms:
- Combine the terms with the imaginary unit, 18i and -28i, and the constant terms, 21 and 24:
(18i - 28i) + (21 + 24) = -10i + 45
So, the simplified expression is -10i + 45.