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

13−5i
13 minus 5 i

1−5i

Answer 1

To simplify \( (7 - \sqrt{-64}) + (6 + 3i) \), we start by simplifying \( \sqrt{-64} \).

We know that: \[ \sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i \]

Now we can substitute this back into the expression: \[ (7 - 8i) + (6 + 3i) \]

Next, we can combine the real parts and the imaginary parts: \[ 7 + 6 + (-8i + 3i) = 13 - 5i \]

So, the simplified form of the expression is: \[ 13 - 5i \]

Thus, the correct response is: 13−5i.