Tuesday, 5 March 2019

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:



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


No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...