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 Nov 2 awarded Popular Question Oct 27 awarded Notable Question Jul 11 awarded Popular Question Aug 23 asked Waves of differing frequency are orthogonal - help me understand Jan 31 awarded Supporter Jan 31 accepted How does $e^{i x}$ produce rotation around the imaginary unit circle? Jan 31 comment How does $e^{i x}$ produce rotation around the imaginary unit circle? Ok, I think this helps me understand it. As you raise i to integer powers, it ends up rotating around the imaginary unit circle: $i^0=1$, $i^1=i$, $i^2=-1$, $i^3=-i$, and $i^4=1$. These positions (1, i, -1, -1) correspond the the following (x,y) positions: (1,0), (0,1), (-1,0), (0,-1). So it makes sense that multiplying the current position by i would result in a 90 degree ($\pi/2$) rotation. Jan 31 awarded Student Jan 31 awarded Editor Jan 31 comment How does $e^{i x}$ produce rotation around the imaginary unit circle? Oops. Yep. Fixed. Jan 31 revised How does $e^{i x}$ produce rotation around the imaginary unit circle? deleted 7 characters in body Jan 31 comment How does $e^{i x}$ produce rotation around the imaginary unit circle? @manu-fatto The exponential function is simply e (2.718...) raised to a power. Jan 31 revised How does $e^{i x}$ produce rotation around the imaginary unit circle? edited tags Jan 31 asked How does $e^{i x}$ produce rotation around the imaginary unit circle? Feb 13 awarded Scholar Feb 13 accepted Solving barometric formulae for height Feb 12 comment Solving barometric formulae for height @BenCrowell: Yes, I know I need the 2 equations. One for lower altitudes, and the other for higher. Feb 12 asked Solving barometric formulae for height Feb 12 awarded Autobiographer