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

Answer 1

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

1. Simplify \(-\sqrt{49} + 5i\):

   • \(\sqrt{49} = 7\)
   • Therefore, \(-\sqrt{49} = -7\).
   • So, this part becomes \(-7 + 5i\).

2. Simplify \(8 - \sqrt{4}\):

   • \(\sqrt{4} = 2\)
   • Therefore, \(8 - \sqrt{4} = 8 - 2 = 6\).

Now we can combine the two parts:

\[ (-7 + 5i) + 6 = -7 + 6 + 5i = -1 + 5i. \]

Thus, the simplified expression is:

\[ \boxed{-1 + 5i}. \]