Quote: complex imaginary powers are the same as sine and cosine; they oscillate; for small t, e^it = 1+it; for small t, cos t is nearly 1 and sin t is nearly 0

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To further investigate the subject of taking complex … So we see that the numbers x and … enough to explain, because if a certain power … again … We also know that for small t, e^it … nearly t, and so it goes, that all … which come from taking imaginary powers, are the … [p.22-10] We summarize with this, the most remarkable …   Google-1   Google-2

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Quote: the most remarkable formula in mathematics: e^i \theta = cos \theta + i sin \theta

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Group: mathematics   (23 topics, 554 quotes)