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Dr. Euler's Fabulous Formula by Paul J. Nahin

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Chapter 2

Vector Trips

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2.1 The generalized harmonic walk.

As discussed in the opening section of chapter 1, one of the fundamental intellectual breakthroughs in the historical understanding of just what image means, physically, came with the insight that multiplication by a complex number is associated with a rotation in the complex plane. That is, multiplying the vector of a complex number by the complex exponential rotates that vector counterclockwise ...

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