Asked by hudson
Use the properties of complex numbers to simplify (−49−−−−√+5i)+(8−−4−−−√) .(1 point)
Responses
8+5i+−53−−−−√
8 plus 5 i plus Start Root negative 53 End Root
8+14i
8 plus 14 i
8+10i
8 plus 10 i
13+9i
Responses
8+5i+−53−−−−√
8 plus 5 i plus Start Root negative 53 End Root
8+14i
8 plus 14 i
8+10i
8 plus 10 i
13+9i
Answers
Answered by
GPT-4o mini
Let's simplify the expression \((-\sqrt{49} + 5i) + (8 - \sqrt{4})\).
First, we simplify each part:
1. \(-\sqrt{49}\) simplifies to \(-7\).
2. \(\sqrt{4}\) simplifies to \(2\).
Now, substituting these values into the expression:
\[
(-7 + 5i) + (8 - 2)
\]
Now, simplify the real parts:
\[
-7 + 8 - 2 = -7 + 6 = -1
\]
Thus, combining both parts, we get:
\[
-1 + 5i
\]
Now, since none of the provided options match \(-1 + 5i\), let's check the responses. It seems there may be a misunderstanding. Based on the provided options, here’s a final check of each response:
1. \(8 + 5i + \sqrt{-53}\)
2. \(8 + 14i\)
3. \(8 + 10i\)
4. \(13 + 9i\)
We realize there may have been an additional error. Let's re-evaluate:
From the beginning, combining the terms:
\[
(-7 + 5i) + (8 - 2) = (-7 + 5i) + 6
\]
\[
= -1 + 5i
\]
The original calculations confirm \(-1 + 5i\). Please verify if you've gotten the problem correctly or if there's a missing component. Based on the calculations, none of the listed results is \( -1 + 5i \).
First, we simplify each part:
1. \(-\sqrt{49}\) simplifies to \(-7\).
2. \(\sqrt{4}\) simplifies to \(2\).
Now, substituting these values into the expression:
\[
(-7 + 5i) + (8 - 2)
\]
Now, simplify the real parts:
\[
-7 + 8 - 2 = -7 + 6 = -1
\]
Thus, combining both parts, we get:
\[
-1 + 5i
\]
Now, since none of the provided options match \(-1 + 5i\), let's check the responses. It seems there may be a misunderstanding. Based on the provided options, here’s a final check of each response:
1. \(8 + 5i + \sqrt{-53}\)
2. \(8 + 14i\)
3. \(8 + 10i\)
4. \(13 + 9i\)
We realize there may have been an additional error. Let's re-evaluate:
From the beginning, combining the terms:
\[
(-7 + 5i) + (8 - 2) = (-7 + 5i) + 6
\]
\[
= -1 + 5i
\]
The original calculations confirm \(-1 + 5i\). Please verify if you've gotten the problem correctly or if there's a missing component. Based on the calculations, none of the listed results is \( -1 + 5i \).