Euler's Formula

From GM-RKB
(Redirected from Euler's formula)
Jump to navigation Jump to search

A Euler's Formula is a mathematical equation (A=B) where A is a complex exponential function and B is the sum of trigonometric functions.

  • Context
    • It can be defined as [math]\displaystyle{ e^{ix}=cosx + i sinx }[/math] , for any real number [math]\displaystyle{ x }[/math]
  • Example(s):
    • [math]\displaystyle{ z=re^{i\theta}=r(cos\theta+isin\theta) }[/math]
    • [math]\displaystyle{ e^{i\pi}=cos(\pi)+isin(\pi)= -1 +i0= -1 }[/math]
    • [math]\displaystyle{ e^{i\pi/2}=cos(\pi/2)+isin(\pi/2)= 0+i1=i }[/math]
  • Counter-Example(s):
    • [math]\displaystyle{ e^{2}= 7.3891 }[/math]
    • [math]\displaystyle{ |3+i4|=\sqrt{3^2+4^2}=5 }[/math]
  • See: Complex Exponential Function, Euler Characteristic, Complex Number, Exponential Function, Imaginary Unit.


References

2015