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Simplify: (4-3i)-5(-2+7i)+(8+7i). You may use a calculator to check your work, but please write out all work in order to receive full credit.

User Tom Busby
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1 Answer

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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.

User Srikanth Balaji
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