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The Limit That Looks Impossible… But Isn’t.
Автор: Math Quest Club
Загружено: 2026-01-20
Просмотров: 110
Описание:
This limit looks like pure chaos: a complex number, an n² exponent, and a mysterious counter-rotation.
limₙ→∞ (1 + i/n)ⁿ² · e⁻ⁱⁿ
You’d expect it to spin forever and never settle… but with the right trick, the runaway rotation cancels out and a clean constant appears.
In this video we use:
• complex-plane intuition (rotation + magnitude)
• a natural log transformation
• Taylor series as a “microscope” near 0
• a perfect cancellation that reveals the final answer
Spoiler (final result): √e
#complexnumbers #limits #calculus #mathematics #math #taylorseries #euler #analysis #mathvideo #learnmath #shortmath #imaginarynumbers #mathquestclub
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