XiXiDu comments on More intuitive explanations! - Less Wrong

22 Post author: XiXiDu 06 January 2012 06:10PM

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Comment author: XiXiDu 06 January 2012 06:32:19PM *  0 points [-]

5) Proof of Euler's formula using power series expansions.

I forgot that this is only insightful if you already realized the following:

  • (3+4i) =
  • (r, angel) =
  • (sqrt((3^2)+(4^2)), arctan(4/3)) =
  • (5, 53.1301) =
  • r(cos(x)+isin(x)) =
  • 5(cos(arctan(4/3))+isin(arctan(4/3))) =
  • 5e^(arctan(4/3)*i) =
  • e^ln(5)*e^(arctan(4/3)i) =
  • e^(ln(5)+arctan(4/3)i)
Comment author: ZankerH 07 January 2012 12:42:34PM 0 points [-]

Only the cartesian, polar and cos-sin forms were obvious to me, and I was still able to make sense of the Taylor series proof.

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