Use the properties of complex numbers to simplify (−49−−−−√+5i)+(8−−4−−−√) .(1 point)

Question

Responses

8+5i+−53−−−−√
8 plus 5 i plus Start Root negative 53 End Root

8+14i
8 plus 14 i

8+10i
8 plus 10 i

13+9i

Answer 1

Let's simplify the expression \((-\sqrt{49} + 5i) + (8 - \sqrt{4})\).

First, we simplify each part:

1. \(-\sqrt{49}\) simplifies to \(-7\).
2. \(\sqrt{4}\) simplifies to \(2\).

Now, substituting these values into the expression:

\[ (-7 + 5i) + (8 - 2) \]

Now, simplify the real parts:

\[ -7 + 8 - 2 = -7 + 6 = -1 \]

Thus, combining both parts, we get:

\[ -1 + 5i \]

Now, since none of the provided options match \(-1 + 5i\), let's check the responses. It seems there may be a misunderstanding. Based on the provided options, here’s a final check of each response:

1. \(8 + 5i + \sqrt{-53}\)
2. \(8 + 14i\)
3. \(8 + 10i\)
4. \(13 + 9i\)

We realize there may have been an additional error. Let's re-evaluate:

From the beginning, combining the terms:
\[ (-7 + 5i) + (8 - 2) = (-7 + 5i) + 6 \]

\[ = -1 + 5i \]

The original calculations confirm \(-1 + 5i\). Please verify if you've gotten the problem correctly or if there's a missing component. Based on the calculations, none of the listed results is \( -1 + 5i \).