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Boost Productivity Fast—Get the Ultimate Windows 10 Assessment Kit Today! - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Let \( a \) and \( b \) be complex numbers such that \( a + b = 4 + 2i \) and \( ab = 5 + 3i \). Find the value of \( a^2 + b^2 \).

📌 We start with the identity for the square of a sum:

📌 Rearranging gives:

📌 a^2 + b^2 = (a + b)^2 - 2ab

📌 Substitute the given values \( a + b = 4 + 2i \) and \( ab = 5 + 3i \):

📌 a^2 + b^2 = (4 + 2i)^2 - 2(5 + 3i)

📌 First, compute \( (4 + 2i)^2 \):

📌 Now compute \( 2(5 + 3i) = 10 + 6i \).

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