Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to get an intuitive grasp of the Euler Relationship

e^i(theta)=cos(theta)+i sin(theta)

and also understand how to graph the exponential spiral, as demonstrated on this web page:

http://www-math.mit.edu/daimp/ComplexExponential.html"

Ok, first the neuron stimulation.

I grasp how cos corresponds to the Real axis of the unit circle and sin is the imaginary axis. I grasp how to plot a complex number on the imaginary plane.

I don't graspwhycos(theta) + i sin(theta) gives me a pointonthe unit circle, when on a real plane I'd have to invoke Pythagoras: sqrt((cos(theta))^2 + (sin(theta))^2) = 1 to get a pointonthe circle.

Regarding the complex exponential tool at the link above, when I try to calculate the "a" and "b" calculations on the right side using the "a" and "b" selections on the left side, I get confused. For example, if I set b=0 and adjust a on the left, on the right side I get just e^a. This is obvious even to me. If I set a=0 and adjust b on the left, then on the right side, "a" is cos(left b) and "b" is sin(left b), so left-side b really is theta. I follow so far. How do I calculate the right-side a and b when the left-side a and b are not zero?

More fundamentally, how do you guys mentally picture what the function e^ix looks like? I want to picture a circle, but I'm not getting it.

Sigh.

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# Graphing Euler Relationship as exponential spiral

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