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Perform the indicated operation \& simplify. \( (-7 i)(2 i)=\square \)

Ask by Tyler Mann. in the United States
Feb 03,2025

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\[ (-7i)(2i) = 14 \]

Solución

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:** \[ (-7i)(2i) = 14 \]

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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 \(14\).

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