Final answer:
To simplify (4-3i)-5(-2+7i)+(8+7i), distribute -5 to the terms in the second parenthesis, combine like terms, getting the final answer 22 - 31i.
Step-by-step explanation:
To simplify the expression (4-3i)-5(-2+7i)+(8+7i), we can combine like terms. Apply the distributive property to the second term by multiplying -5 with each of the terms inside the parentheses, and then add all the real numbers and imaginary numbers separately.
- (4 - 3i) becomes 4 - 3i.
- -5(-2 + 7i) becomes 10 - 35i when we distribute the -5.
- (8 + 7i) remains the same.
Now combine the real parts and the imaginary parts:
Real parts: 4 + 10 + 8 = 22
Imaginary parts: -3i - 35i + 7i = -31i
Putting it all together, we get:
22 - 31i
To check if the answer is reasonable, verify that all like terms were combined properly and that the operations were done correctly.