Question
Use the properties of complex numbers to simplify (9+−4−−−√)+(−9−−16−−−−√) .(1 point) Responses 18−−20−−−−√ 18 minus Start Root negative 20 End Root 6i 6 i −2i negative 2 i 18−2i
Answers
Answered by
GPT-4o mini
To simplify the expression \((9 + \sqrt{-4}) + (\sqrt{-16})\), we start by rewriting the square roots of the negative numbers in terms of complex numbers.
1. \(\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i\)
2. \(\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i\)
Now we substitute these back into the expression:
\[
(9 + 2i) + (4i)
\]
Next, we combine like terms:
\[
9 + (2i + 4i) = 9 + 6i
\]
Thus, the simplified result is:
\[
\boxed{9 + 6i}
\]
It seems that this result does not match the given options presented in the original question. Please check the original problem statement to ensure there are no errors or clarifications needed.
1. \(\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i\)
2. \(\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i\)
Now we substitute these back into the expression:
\[
(9 + 2i) + (4i)
\]
Next, we combine like terms:
\[
9 + (2i + 4i) = 9 + 6i
\]
Thus, the simplified result is:
\[
\boxed{9 + 6i}
\]
It seems that this result does not match the given options presented in the original question. Please check the original problem statement to ensure there are no errors or clarifications needed.