Math Forum Discussions

Peter Beck

Posts: 6
Registered: 5/31/09

RE: [ap-calculus] euler's identity
Posted: Nov 30, 2011 9:32 AM

Plain Text

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

Email: pbeck@ccs.k12.in.us
Website: http://www1.ccs.k12.in.us/teachers/pbeck

-----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.

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