Question
Perform the indicated operation \& simplify. \( (-7 i)(2 i)=\square \)
Ask by Tyler Mann. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
(-7i)(2i) = 14
\]
Solution
To perform the operation \( (-7i) \times (2i) \) and simplify, follow these steps:
1. **Multiply the coefficients (numbers) together:**
\[
(-7) \times 2 = -14
\]
2. **Multiply the imaginary units \( i \times i \):**
\[
i \times i = i^2
\]
Recall that \( i^2 = -1 \).
3. **Combine the results:**
\[
-14 \times i^2 = -14 \times (-1) = 14
\]
**Final Answer:**
\[
(-7i)(2i) = 14
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
When you multiply the complex numbers \((-7 i)\) and \((2 i)\), you multiply the coefficients and then the imaginary units. So, \((-7)(2) = -14\) and \(i \times i = i^2\). Since \(i^2 = -1\), the calculation becomes: \[ (-7 i)(2 i) = -14 i^2 = -14(-1) = 14. \] Thus, the simplified result is \(14\).
