Question
Use the properties of complex numbers to simplify (−49−−−−√+5i)+(8−−4−−−√)
.(1 point)
Responses
8+10i
8 plus 10 i
8+14i
8 plus 14 i
13+9i
13 plus 9 i
8+5i+−53−−−−√
8 plus 5 i plus Start Root negative 53 End Root
.(1 point)
Responses
8+10i
8 plus 10 i
8+14i
8 plus 14 i
13+9i
13 plus 9 i
8+5i+−53−−−−√
8 plus 5 i plus Start Root negative 53 End Root
Answers
Answered by
GPT-4o mini
To simplify the expression \((-\sqrt{49} + 5i) + (8 - \sqrt{4})\), let's break it down step by step.
1. **Calculate \(-\sqrt{49}\)**:
\[
-\sqrt{49} = -7
\]
2. **Calculate \(-\sqrt{4}\)**:
\[
-\sqrt{4} = -2
\]
Now substitute these values back into the expression:
\[
(-7 + 5i) + (8 - 2)
\]
3. **Combine the real parts**:
\[
-7 + 8 - 2 = -7 + 6 = -1
\]
4. **Combine the imaginary parts**:
\[
5i
\]
So combining both results gives us:
\[
-1 + 5i
\]
However, this isn't one of the answers. Let’s check assuming we might have misperformed some of the calculations originally.
Looking at the provided responses, let's evaluate if misunderstood the operations or the question’s parts:
So, performing the calculation correctly:
- From the original assumption and breakdown, our total comes to:
\[
-1 + 5i
\]
The correct format from options would indeed not yield a satisfactory answer based on your set-up. Let’s double-check on another level of simplification:
Given all roots:
\[
(-7 + 5i) + (8 - 2) \Rightarrow -1 + 5i \quad \text{(confirms)}
\]
This is indeed: \( -1 + 5i \).
None appear direct matches present specifically in the options you noted. Thus reviewing further might lead us back to validating specifics or context on keeping choice responses expected.
Final answer reconciliation available doesn’t lead to presented matched formats directly implying internal review may align mismatch context.
Given choices only seem valid translations/sum yet lack match. Final resulting confirmatively stated is:
\[
-1 + 5i
\]
Confirming earlier.
Ensure other context isn't being overlooked for multiple-choice guideline from firm header unless expanded or variants in system initially bring forward consideration!
1. **Calculate \(-\sqrt{49}\)**:
\[
-\sqrt{49} = -7
\]
2. **Calculate \(-\sqrt{4}\)**:
\[
-\sqrt{4} = -2
\]
Now substitute these values back into the expression:
\[
(-7 + 5i) + (8 - 2)
\]
3. **Combine the real parts**:
\[
-7 + 8 - 2 = -7 + 6 = -1
\]
4. **Combine the imaginary parts**:
\[
5i
\]
So combining both results gives us:
\[
-1 + 5i
\]
However, this isn't one of the answers. Let’s check assuming we might have misperformed some of the calculations originally.
Looking at the provided responses, let's evaluate if misunderstood the operations or the question’s parts:
So, performing the calculation correctly:
- From the original assumption and breakdown, our total comes to:
\[
-1 + 5i
\]
The correct format from options would indeed not yield a satisfactory answer based on your set-up. Let’s double-check on another level of simplification:
Given all roots:
\[
(-7 + 5i) + (8 - 2) \Rightarrow -1 + 5i \quad \text{(confirms)}
\]
This is indeed: \( -1 + 5i \).
None appear direct matches present specifically in the options you noted. Thus reviewing further might lead us back to validating specifics or context on keeping choice responses expected.
Final answer reconciliation available doesn’t lead to presented matched formats directly implying internal review may align mismatch context.
Given choices only seem valid translations/sum yet lack match. Final resulting confirmatively stated is:
\[
-1 + 5i
\]
Confirming earlier.
Ensure other context isn't being overlooked for multiple-choice guideline from firm header unless expanded or variants in system initially bring forward consideration!