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heta_1 - heta_2 \equiv 60^\circ \pmod180^\circ, - AMAZONAWS
heta_1 - heta_2 \equiv 60^\circ \pmod180^\circ, - AMAZONAWS
📅 March 6, 2026
👤 scraface
Mar 06, 2026
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📌 Solution: Use identity $ p^2 + q^2 = (p + q)^2 - 2pq $. Substituting: $ 10 - 24i = (3 + 4i)^2 - 2pq $. Compute $ (3 + 4i)^2 = 9 + 24i - 16 = -7 + 24i $. Then $ 10 - 24i = -7 + 24i - 2pq $. Rearranging: $ 17 - 48i = -2pq \Rightarrow pq = \frac{-17 + 48i}{2} $. \boxed{-\dfrac{17}{2} + 24i}
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