A Shot of Elegance: Part 2

Calculus Level 2

What is the principal value of i i ? i^i?


The answer is 0.207879576.

Steven Zheng by Steven Zheng , 26, China

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1 solution

Steven Zheng
Jul 16, 2014

From Euler-de Moivre formula e i x = c o s x + i s i n x . { e }^{ ix } = cos x +isin x. We will answer this most straightforwardly with x = π . x = \pi. Then e i π = − 1. { e }^{ i\pi } = -1. Take the square root and exponentiate by i i = e − π / 2 , i^ i = { e }^{ -\pi/2 }, which is about 0.208.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I added "principal value" to your question.

Note that the final equality is wrong. You most probably mean i i = e − π / 2 i^i = e^{ - \pi/2 } .

Calvin Lin Staff - 6 years, 11 months ago

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I fixed the last equation. Thanks.

Steven Zheng - 6 years, 11 months ago

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