Question

BRAIN TESTER 01.

PROVE THAT :-


${e}^{\pi \: i} = ( - 1)$

Thanks!!

Answer 1

Answer :

Using Complex numbers theorem, we get

eⁱˣ = cosx + i sinx ...(i)

Let us take x = π

From (i), we get

e^(i π) = cosπ + i sinπ

= - 1 + 0, since cosπ = - 1 and sinπ = 0

or, e^(i π) = - 1

Hence, proved.

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