Question

Simplify the following expression.

left-parenthesis negative 2 plus 4 i right-parenthesis minus left-parenthesis 3 minus 5 i right-parenthesis
(1 point)
Responses

negative 5 minus i
Image with alt text: negative 5 minus i

negative 1 minus i
Image with alt text: negative 1 minus i

negative 1 plus 9 i
Image with alt text: negative 1 plus 9 i

negative 5 plus 9 i

Answer 1

that incorrect

Answer 2

To simplify the expression \(( -2 + 4i ) - ( 3 - 5i )\), we follow these steps:

1. Distribute the negative sign to the second term:
\[
-2 + 4i - 3 + 5i
\]

2. Combine like terms:
- Combine the real parts: \(-2 - 3 = -5\)
- Combine the imaginary parts: \(4i + 5i = 9i\)

So, the simplified expression is:
\[
-5 + 9i
\]

Therefore, the answer is **negative 5 plus 9 i**.

Answer 3

Let's re-evaluate the expression step by step to ensure the right answer.

Given the expression:
\[
(-2 + 4i) - (3 - 5i)
\]

1. Distribute the negative sign across the second term:
\[
-2 + 4i - 3 + 5i
\]

2. Now combine the real parts and the imaginary parts separately:
- Real parts: \(-2 - 3 = -5\)
- Imaginary parts: \(4i + 5i = 9i\)

So, the overall result is:
\[
-5 + 9i
\]

Thus, the final, simplified expression is indeed:
\[
\text{negative } 5 \text{ plus } 9i
\]

If you have a different answer in mind or there’s a misunderstanding, please let me know!