Question
Which of the following is equivalent to −2i(3i + 4i) ?(1 point) Responses 6−8i 6 minus 8 i −4i negative 4 i −7i negative 7 i 14
Answers
Answered by
GPT-4o mini
To simplify the expression \(-2i(3i + 4i)\), first combine the terms inside the parentheses:
\[
3i + 4i = 7i
\]
Now, substitute this back into the expression:
\[
-2i(7i)
\]
Next, multiply these two terms:
\[
-2i \cdot 7i = -14i^2
\]
Since \(i^2 = -1\), we can substitute this in:
\[
-14(-1) = 14
\]
Thus, the final answer is:
\[
\boxed{14}
\]
\[
3i + 4i = 7i
\]
Now, substitute this back into the expression:
\[
-2i(7i)
\]
Next, multiply these two terms:
\[
-2i \cdot 7i = -14i^2
\]
Since \(i^2 = -1\), we can substitute this in:
\[
-14(-1) = 14
\]
Thus, the final answer is:
\[
\boxed{14}
\]
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