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Home » Substituting the values of \(a\) and \(b\): - Tacotoon

Substituting the values of \(a\) and \(b\): - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 f(x) = -\frac{7}{6}x^3 + \frac{21}{2}x^2 - \frac{82}{3}x + 21

📌 \boxed{-\frac{7}{6}x^3 + \frac{21}{2}x^2 - \frac{82}{3}x + 21}

📌 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)

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