Use the properties of complex numbers to simplify completely (7−−64−−−−√)+(6+3i) .(1 point)

Question

Responses

13+11i
13 plus 11 i

8i
8 i

1−5i
1 minus 5 i

13−5i

Answer 1

To simplify the expression \( (7 - \sqrt{64}) + (6 + 3i) \), we start by simplifying each part:

1. Simplifying \( \sqrt{64} \): \[ \sqrt{64} = 8 \] Therefore, the expression becomes: \[ 7 - \sqrt{64} = 7 - 8 = -1 \]

2. Now rewrite the entire expression: \[ -1 + (6 + 3i) \]

3. Adding the real parts and the imaginary parts: \[ (-1 + 6) + 3i = 5 + 3i \]

At this point, we have simplified the expression to \( 5 + 3i \).

It seems like none of the provided responses match \( 5 + 3i \). Please check if there was a typo in the original expression provided or if there are further calculations needed.