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Home » Simplify: \( 4\pi r^2 = 100\pi \). - Blask

Simplify: \( 4\pi r^2 = 100\pi \). - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Thus, the angular velocity is:

📌 \boxed{\frac{2\pi}{t}}

📌 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

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Résoudre pour \( r \) :
r = \frac{31.4}{2\pi} = \frac{31.4}{6.28} \approx 5 \text{ cm}
Aire \( A = \pi r^2 \) :
A = \pi \times 5^2 = 25\pi \approx 78.5 \text{ cm}^2
#### 78.5 cm²
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