# 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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