Complex Numbers Unlocking Quantum Mechanics and Engineering

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Neil deGrasse Tyson sits down with Grant Sanderson of 3Blue1Brown to demystify the number i = √−1. If “imaginary” makes it sound fake, Grant reframes it as cycle/clock numbers—the natural language for waves, rotations, and frequencies—which is why complex numbers power quantum mechanics and electrical engineering.

They trace how “i” first surfaced while solving cubic equations, worked stunningly well, and only later earned a clear geometric meaning. Grant then gives a quick, visual-friendly taste of circle inversion—treating a circle like a mirror—to show how conformal geometry can turn hard problems into easy ones. @    • What's Up With Imaginary Numbers?