Question

Simplify the expression (−7−−100−−−−√)−(−15−−81−−−−√)
.(1 point)
Responses

8−i
8 minus i

8−19i
8 minus 19 i

−8+i
negative 8 plus i

−22+19i

Answer 1

To simplify the expression \((−7−\sqrt{−100})−(−15−\sqrt{−81})\), let's break it down step by step.

1. First, handle the square roots of the negative numbers:
- \(\sqrt{-100} = \sqrt{100} \cdot \sqrt{-1} = 10i\)
- \(\sqrt{-81} = \sqrt{81} \cdot \sqrt{-1} = 9i\)

2. Replace the square roots in the expression:
\[
(−7−10i)−(−15−9i)
\]

3. Distributing the negative sign in front of the second parenthesis:
\[
−7−10i + 15 + 9i
\]

4. Combine like terms:
- For the real parts: \(-7 + 15 = 8\)
- For the imaginary parts: \(-10i + 9i = -i\)

5. Therefore, the expression simplifies to:
\[
8 - i
\]

Thus, the simplified expression is \(8 - i\).

The correct option is:
**8−i** (8 minus i).