Question
Perform the indicated operation \& simplify. Express the answer in terms of \( i \) (as a complex number). \( (-7 i)(2 i)=\square \)
Ask by Simpson Hart. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((-7i)(2i) = 14\)
Solution
To perform the multiplication \((-7i)(2i)\) and simplify the expression in terms of \(i\), follow these steps:
1. **Multiply the coefficients:**
\[
-7 \times 2 = -14
\]
2. **Multiply the imaginary units:**
\[
i \times i = i^2
\]
Recall that \(i^2 = -1\).
3. **Combine the results:**
\[
-14 \times i^2 = -14 \times (-1) = 14
\]
So, the simplified result is:
\[
(-7i)(2i) = 14
\]
**Answer:** \(14\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To perform the operation \((-7 i)(2 i)\), you multiply the coefficients and the imaginary units separately. First, multiply the coefficients: \(-7 \times 2 = -14\). Next, multiply the \(i\) values: \(i \times i = i^2\). Since \(i^2 = -1\), we have: \((-7 i)(2 i) = -14 \times i^2 = -14 \times (-1) = 14\). Thus, the simplified result is \(14\).
