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When you draw ripples in the complex plane using the distances ∣z − 1∣ and ∣z + 1∣, something surprising happens. 🌊 Let those two circles (centered at −1 and +1) expand so that the total distance satisfies ∣z − 1∣ + ∣z + 1∣ = 4. Every point where the two ripples meet lies on a perfect ellipse — because the sum of the ...
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