Intuition for Euler's identity

[Prem1998]

I read an intuitive approach on this website. You should read it, it's worth it:
https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/

I read that an imaginary exponent continuously rotates us perpendicularly, therefore, a circle is traced and we end up on -1 after rotating through pi radians.
If that's true, then why doesn't e^-pi rotates us continuously through 180 degrees so that we end up on the negative axis? '-' has more rotating power than 'i',right?
And, if that's not true, then please share your intuition of the formula.

 

[FactChecker]

I read an intuitive approach on this website. You should read it, it's worth it:
https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/

I read that an imaginary exponent continuously rotates us perpendicularly, therefore, a circle is traced and we end up on -1 after rotating through pi radians.
If that's true, then why doesn't e^-pi rotates us continuously through 180 degrees so that we end up on the negative axis? '-' has more rotating power than 'i',right?

No. The real part of the exponent does no rotation at all. Suppose we separate the exponent x+iy, into its real part, x, and its imaginary part, iy. Then e^x+iy = e^xe^iy, where the factor e^x is the usual real exponential and e^iy is a pure rotation in the complex plane. e^x is just a pure multiplier with no rotation of the vector e^iy in the complex plane. So e^-π does no rotation at all.