Question
Use the properties of complex numbers to simplify (9+
−4
)+(−9−
−16
).
A. −2i B. 18−2i C. 18−
−20
D. 6i
−4
)+(−9−
−16
).
A. −2i B. 18−2i C. 18−
−20
D. 6i
Answers
Answered by
GPT-4o mini
To simplify the expression \((9 + -4i) + (-9 - -16i)\), we can break it down and combine the real and imaginary parts.
First, rewrite the expression:
\[
(9 - 4i) + (-9 + 16i)
\]
Now, combine the real and imaginary parts separately:
1. **Real parts**: \(9 + (-9) = 0\)
2. **Imaginary parts**: \(-4i + 16i = 12i\)
Now, putting it together, we have:
\[
0 + 12i = 12i
\]
This answer does not match any of the provided options (A, B, C, D).
Let's re-check the problem for any computation errors.
1. \(9 + -4i = 9 - 4i\)
2. \(-9 - -16i = -9 + 16i\)
Combining:
1. Real part: \(9 + (-9) = 0\)
2. Imaginary part: \(-4 + 16 = 12\)
Final result: \(12i\)
Since neither the result \(12i\) nor an equivalent appears in the options listed, there seems to be a discrepancy. However, based on the calculations, the result is confirmed to be \(12i\).
First, rewrite the expression:
\[
(9 - 4i) + (-9 + 16i)
\]
Now, combine the real and imaginary parts separately:
1. **Real parts**: \(9 + (-9) = 0\)
2. **Imaginary parts**: \(-4i + 16i = 12i\)
Now, putting it together, we have:
\[
0 + 12i = 12i
\]
This answer does not match any of the provided options (A, B, C, D).
Let's re-check the problem for any computation errors.
1. \(9 + -4i = 9 - 4i\)
2. \(-9 - -16i = -9 + 16i\)
Combining:
1. Real part: \(9 + (-9) = 0\)
2. Imaginary part: \(-4 + 16 = 12\)
Final result: \(12i\)
Since neither the result \(12i\) nor an equivalent appears in the options listed, there seems to be a discrepancy. However, based on the calculations, the result is confirmed to be \(12i\).