e^(theta*i) allows you to find the value of any theta using the unit circle on the complex plane.
For instance: e^(0*i)=1 because the radian measure is zero yielding the coordinate (1, 0i) e^(pi*i)=-1 because the radian measure is pi yielding the coordinate (-1, 0i)
So e^(pi/2*i) will equal i since the the radian measure is pi/2 yielding the coordinate (0, i).
So to describe e^i, it is the coordinate found by rotating 1 radian on the unit circle in the complex plane.
Peter Beck Carmel High School 520 E Main St. Carmel, IN 46032 846-7721 x7365
-----Original Message----- From: Paul SooHoo [mailto:psoohoo@optonline.net] Sent: Tuesday, November 29, 2011 9:52 PM To: AP Calculus Subject: [ap-calculus] euler's identity
I have a student that asked the meaning of Euler's identity (he said he saw it on a youtube video which astounded me). Beyond the fact that it contains many important mathematical constants it's not clear to me at all how it works i.e. I never took a course in complex analysis.
Is there a simple way of understanding what it means to have e^i or is it too hard to describe without a background in complex analysis.
