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

.(1 point)
Responses

8+14i
8 plus 14 i

8+5i+−53−−−−√
8 plus 5 i plus square root of negative 53

13+9i
13 plus 9 i

8+10i

1 answer

To simplify the expression \((-\sqrt{49} + 5i) + (8 - \sqrt{4})\), we first simplify each part:

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

Now substitute these values back into the expression:

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

Now simplify the real part:

\[ (-7 + 8 - 2) + 5i = (-1) + 5i \]

Combining the terms gives us:

\[ -1 + 5i \]

None of the options given match the simplified expression of \(-1 + 5i\). Therefore, the choices you provided do not reflect the simplified version correctly. The correct outcome is:

\[-1 + 5i\] which is not in your list. Would you like me to help you based on a different set of conditions?