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basic_tools:eulers_formula [2018/04/16 07:50]
jakobadmin ↷ Page moved from basic_notions:eulers_formula to basic_tools:eulers_formula
basic_tools:eulers_formula [2020/04/02 13:44] (current)
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 where $e^{ix}$ denotes the [[basic_tools:​exponential_function|exponential function]] and $ \cos(x)$, $\sin(x)$ are the usual [[basic_tools:​trigonometric_functions|trigonometric functions]]. If we evaluate this equation at $x= \pi$, we get where $e^{ix}$ denotes the [[basic_tools:​exponential_function|exponential function]] and $ \cos(x)$, $\sin(x)$ are the usual [[basic_tools:​trigonometric_functions|trigonometric functions]]. If we evaluate this equation at $x= \pi$, we get
  
-$$ e^{i\pi } = \cos(\pi) + i \sin(\pi) = -i = - ​\, ​ .$$+$$ e^{i\pi } = \cos(\pi) + i \sin(\pi) = -1 -i = - ​\, ​ .$$
  
 This shows a deep relationship between the exponential function, the [[basic_tools:​imaginary_numbers|imaginary unit]] $i$ and $\pi$. (Pi is the ratio between circumference and diameter shared by all circles.) This shows a deep relationship between the exponential function, the [[basic_tools:​imaginary_numbers|imaginary unit]] $i$ and $\pi$. (Pi is the ratio between circumference and diameter shared by all circles.)
basic_tools/eulers_formula.1523857824.txt.gz · Last modified: 2018/04/16 05:50 (external edit)