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Home » The Missing Formula Behind the Area of a Semicircle You NEED to Know! - Databee Business Systems

The Missing Formula Behind the Area of a Semicircle You NEED to Know! - Databee Business Systems

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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\[ \text{Discriminant} = 2i - 4i = -2i \]
Now, compute \( \sqrt{-2i} \). Let \( \sqrt{-2i} = a + bi \), then:
\[ (a + bi)^2 = a^2 - b^2 + 2abi = -2i \]
\[ a^2 - b^2 = 0 \quad \text{(1)} \]
\[ 2ab = -2 \quad \text{(2)} \]
From (1): \( a^2 = b^2 \Rightarrow a = b \) or \( a = -b \)
Try \( a = b \):
Then (2): \( 2a^2 = -2 \Rightarrow a^2 = -1 \) — not possible in reals...
Try \( a = -b \):
Let \( b = -a \), then (2): \( 2a(-a) = -2a^2 = -2 \Rightarrow a^2 = 1...

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