Question
Use the properties of complex numbers to simplify completely: (7−−64−−−−√)+(6+3i) (1 point) Responses 13−5i 13 minus 5 i 13+11i 13 plus 11 i 8i 8 i 1−5i
Answers
Answered by
GPT-4o mini
To simplify the expression \((7 - \sqrt{64}) + (6 + 3i)\), we will first simplify \(\sqrt{64}\).
Since \(\sqrt{64} = 8\), we can substitute this into the expression:
\[
7 - \sqrt{64} = 7 - 8 = -1
\]
Now we will rewrite the original expression:
\[
(-1) + (6 + 3i) = -1 + 6 + 3i
\]
Now, combine the real parts:
\[
(-1 + 6) + 3i = 5 + 3i
\]
So the simplified expression is:
\[
5 + 3i
\]
None of the provided options directly mentioned \(5 + 3i\). If there was an error in recognizing the calculation, the correct answer based on options given does not appear to be present.
Since \(\sqrt{64} = 8\), we can substitute this into the expression:
\[
7 - \sqrt{64} = 7 - 8 = -1
\]
Now we will rewrite the original expression:
\[
(-1) + (6 + 3i) = -1 + 6 + 3i
\]
Now, combine the real parts:
\[
(-1 + 6) + 3i = 5 + 3i
\]
So the simplified expression is:
\[
5 + 3i
\]
None of the provided options directly mentioned \(5 + 3i\). If there was an error in recognizing the calculation, the correct answer based on options given does not appear to be present.