Use the properties of complex numbers to simplify (9+

Question

−4
​
)+(−9−
−16
​
).
A. −2i B. 18−2i C. 18−
−20
​
D. 6i

Answer 1

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 \(12i\).