Simplify the expression (−7−−100−−−−√)−(−15−−81−−−−√)

Question

.(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).