Question

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.