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This exploration leads calculus students, discussing the work in trios or quartets, to formulate Euler's Identity: e^(ipi)+1=0, a beautiful equation holding 5 important numbers (0,1,e,pi,i the imaginary root of -1) and the basic operations of adding, multiplying, and exponentiation. When can you give this to students? After they know the basic trig derivatives & quotient rule. There are other lessons where you prove the same formula with infinite series for sin x & cos x, but this introduces the equation earlier in the course of calculus, to inspire students to study some of beautiful topics in Calculus C and Complex Analysis in college. Hat tip to Dr. Roberto Martinez for showing me this proof, which I put in worksheet form.
This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2003-12-14.
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