A Subtle Error

Algebra Level 2

I will attempt to prove that \(\pi = -\pi \). In which of these steps did I make a flaw in my logic?

Step 1: Using a famous theorem, \[e^{i\pi } = -1 . \] Step 2: Reciprocate both sides of the equation: \[e^{-i\pi} = \dfrac{1}{-1} = -1 . \] Step 3: Equating both equations in the above two steps gives \[ \large e^{i \pi} = e^{-i \pi} . \] Step 4: Since the bases are the same, \[ i \pi = -i \pi . \] Step 5: Canceling the imaginary number yields \[ \pi = -\pi .\]

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