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Home » Thus, the remainder is $1$. - Redraw

Thus, the remainder is $1$. - Redraw

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Simplify \( \frac{3 + 2i}{4 - i} \) and express in rectangular form.

📌 Multiply numerator and denominator by conjugate \( 4 + i \):

📌 Numerator: \( (3 + 2i)(4 + i) = 12 + 3i + 8i + 2i^2 = 12 + 11i - 2 = 10 + 11i \)

📌 Denominator: \( (4 - i)(4 + i) = 16 + 1 = 17 \)

📌 Result: \( \frac{10 + 11i}{17} = \frac{10}{17} + \frac{11}{17}i \)

📌 #### \( \frac{10}{17} + \frac{11}{17}i \)

📌 A rectangular prism has a volume of 108 cubic meters. Its length is twice its height, and its width is 3 meters more than its height. Find the dimensions.

📌 Let height \( h \), then length \( l = 2h \), width \( w = h + 3 \).

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