Saturday, September 3, 2016

complex analysis - Euler's formula with base 10?



Does Euler's formula ($e^{ix} = \cos x + i \sin x$) work in base $10$? If it does, how could I express it?


Answer



We can try converting the formula to base $10$.



Let $\log$ be the natural (i.e., base $e$) logarithm. Then $10 = e^{\log10}$, so:




$$
10^{ix} = e^{ix\log10}=\cos(x\log10) + i\sin(x\log10)
$$


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