Question
Use the properties of complex numbers to simplify (−49−−−−√+5i)+(8−−4−−−√)
(1 point)
Responses
8+14i
8 plus 14 i
13+9i
13 plus 9 i
8+10i
8 plus 10 i
8+5i+−53−−−−√
(1 point)
Responses
8+14i
8 plus 14 i
13+9i
13 plus 9 i
8+10i
8 plus 10 i
8+5i+−53−−−−√
Answers
Answered by
GPT-4o mini
To simplify the expression \((-49^{1/2}+5i)+(8-4^{1/2})\), let's break it down step by step.
1. First, simplify \(-49^{1/2}\):
\[
-49^{1/2} = -\sqrt{49} = -7.
\]
2. Next, we substitute \(-7\) into the expression:
\[
(-7 + 5i) + (8 - 4^{1/2}).
\]
3. Now simplify \(-4^{1/2}\):
\[
-4^{1/2} = -\sqrt{4} = -2.
\]
4. Substitute \(-2\) back into the expression:
\[
(-7 + 5i) + (8 - 2).
\]
5. Combine the real parts:
\[
-7 + 8 - 2 = -1.
\]
6. The imaginary part remains:
\[
5i.
\]
7. Thus, combining everything gives:
\[
-1 + 5i.
\]
So the simplification of the expression is:
\[
-1 + 5i.
\]
However, none of the response options in your question exactly match this result, which suggests there may have been a miscalculation in the given options. If you'd like to check specific values or calculations, feel free to ask!
1. First, simplify \(-49^{1/2}\):
\[
-49^{1/2} = -\sqrt{49} = -7.
\]
2. Next, we substitute \(-7\) into the expression:
\[
(-7 + 5i) + (8 - 4^{1/2}).
\]
3. Now simplify \(-4^{1/2}\):
\[
-4^{1/2} = -\sqrt{4} = -2.
\]
4. Substitute \(-2\) back into the expression:
\[
(-7 + 5i) + (8 - 2).
\]
5. Combine the real parts:
\[
-7 + 8 - 2 = -1.
\]
6. The imaginary part remains:
\[
5i.
\]
7. Thus, combining everything gives:
\[
-1 + 5i.
\]
So the simplification of the expression is:
\[
-1 + 5i.
\]
However, none of the response options in your question exactly match this result, which suggests there may have been a miscalculation in the given options. If you'd like to check specific values or calculations, feel free to ask!