Complex exponentials spin

When we put time up in the exponent of a complex exponential, the complex number it represent rotates in a circle on the complex plane. You can think of it as a spinning number!

[SlovenskiVuk]

The point of the cos(wt)=1/2(e^jwt+e^-jwt) is that both e numbers move at the same angular speed of w in opposite direction. That makes complex component on the y axis(otherwise jsin(wt)) cancel each other out, which leaves two cos(wt) projections, we devide it by 2 and it gives us the cos(wt) value.

[curtpiazza]

Great presentation! I like how you tie in the concepts to electrical signals. Give you a good background for EE!

[imrozzahan]

Learn this if you want to learn quantum mechanics. Great!

[Titurel]

Life for students would be easier it instead of calling them imaginary numbers they were call rotational numbers

[DarkOdyssey_]

Omega is angular frequency, with the unit rad/sec, not normal frequency

[debendragurung]

ok but what does (+) operatioin imply here..

[curtpiazza]

Great SPIN on an often confusing topic! 😊🎉

[antoniussugianto]

Can someone explain what 3^i and i^i mean exactly geometrically in the complex plane ?

[harkankarakaya]

Why are you trying to turn sine against cosine?