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Home » We check two-digit numbers \( k \equiv 2 \pmod7 \): they are: - Sterling Industries

We check two-digit numbers \( k \equiv 2 \pmod7 \): they are: - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 Question:** A science fiction writer describes a planet where two force fields, modeled by complex numbers \(z_1 = 3 + 4i\) and \(z_2 = 1 - 2i\), interact. Compute the product of these two force fields.

📌 To find the product of the two complex numbers \(z_1\) and \(z_2\), we use the distributive property of multiplication for complex numbers:

📌 z_1 \cdot z_2 = (3 + 4i)(1 - 2i)

📌 Expanding this, we get:

📌 = 3 \cdot 1 + 3 \cdot (-2i) + 4i \cdot 1 + 4i \cdot (-2i)

📌 = 3 - 6i + 4i - 8i^2

📌 Recall that \(i^2 = -1\). Substituting, we have:

📌 = 3 - 6i + 4i + 8

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