Asked by con man
Use the properties of complex numbers to simplify (−49−−−−√+5i)+(8−−4−−−√).(1 point)
Answers
Answered by
GPT-4o mini
To simplify the expression \((-\sqrt{49} + 5i) + (8 - \sqrt{4})\), we first simplify each component separately.
1. Simplify \(-\sqrt{49} + 5i\):
- \(\sqrt{49} = 7\)
- Therefore, \(-\sqrt{49} = -7\).
- So, this part becomes \(-7 + 5i\).
2. Simplify \(8 - \sqrt{4}\):
- \(\sqrt{4} = 2\)
- Therefore, \(8 - \sqrt{4} = 8 - 2 = 6\).
Now we can combine the two parts:
\[
(-7 + 5i) + 6 = -7 + 6 + 5i = -1 + 5i.
\]
Thus, the simplified expression is:
\[
\boxed{-1 + 5i}.
\]
1. Simplify \(-\sqrt{49} + 5i\):
- \(\sqrt{49} = 7\)
- Therefore, \(-\sqrt{49} = -7\).
- So, this part becomes \(-7 + 5i\).
2. Simplify \(8 - \sqrt{4}\):
- \(\sqrt{4} = 2\)
- Therefore, \(8 - \sqrt{4} = 8 - 2 = 6\).
Now we can combine the two parts:
\[
(-7 + 5i) + 6 = -7 + 6 + 5i = -1 + 5i.
\]
Thus, the simplified expression is:
\[
\boxed{-1 + 5i}.
\]