Why does eiπ2=i?

Helen Lewis

Helen Lewis

Answered

2022-01-16

Why does eiπ2=i?

Answer & Explanation

Donald Cheek

Donald Cheek

Expert

2022-01-17Added 41 answers

eiθcosθ+isinθ
This is an IDENTITY, meaning for whatever value of θ.LHS=RHS.
Using θ=12π,
LHS=ei12π
RHS=cos(12π)+isin(12π)
=0+i(1)
=i
Ronnie Schechter

Ronnie Schechter

Expert

2022-01-18Added 27 answers

Start with Eulers
alenahelenash

alenahelenash

Expert

2022-01-24Added 366 answers

eix2=ieiπ=ieiπ2=i2eiπ=1eiπ+1=0 which is Euler's identity

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