Use the properties of complex numbers to simplify (−49−−−−√+5i)+(8−−4−−−√).(1 point)%0D%0AResponses%0D%0A%0D%0A8+14i%0D%0A8 plus 14 i%0D%0A%0D%0A8+5i+−53−−−−√%0D%0A8 plus 5 i plus Start Root negative 53 End Root%0D%0A%0D%0A8+10i%0D%0A8 plus 10 i%0D%0A%0D%0A13+9i%0D%0A13 plus 9 i

Answer 1

To simplify \((-\sqrt{-49} + 5i) + (8 - \sqrt{4})\), let's break it down step by step.

1. Simplify \(-\sqrt{-49}\): \[ -\sqrt{-49} = -\sqrt{49}i = -7i \]

2. Simplify \(-\sqrt{4}\): \[ -\sqrt{4} = -2 \]

3. Now substitute these back into the equation: \[ (-7i + 5i) + (8 - 2) \]

4. Combine like terms:

   • For the imaginary parts: \[ -7i + 5i = -2i \]
   • For the real parts: \[ 8 - 2 = 6 \]

5. Combine the results: \[ 6 - 2i \]

None of the provided responses match \(6 - 2i\). Please double-check the original expression and values to ensure correct classification and simplification.