Use the properties of complex numbers to simplify completely (7−−64−−−−√)+(6+3i) .(1 point) Responses 13−5i 13 minus 5 i 8i 8 i 1−5i 1 minus 5 i 13+11i

Answer 1

To simplify the expression \((7 - \sqrt{64}) + (6 + 3i)\), let's break it down step by step.

1. Calculate the square root: \(\sqrt{64} = 8\)

2. Substitute back into the expression: \[ (7 - 8) + (6 + 3i) \]

3. Simplify further: \[ -1 + (6 + 3i) = -1 + 6 + 3i = 5 + 3i \]

The simplified expression is \(5 + 3i\).

However, checking against the provided options:

• 13 - 5i
• 8i
• 1 - 5i
• 13 + 11i

None of the options match \(5 + 3i\). It's possible that the original expression may not have been transcribed or simplified correctly. Please double-check if the expression to be simplified was written correctly.