A Subtle Error

Algebra Level 2

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

Step 1: Using a famous theorem, eiπ=1.e^{i\pi } = -1 . Step 2: Reciprocate both sides of the equation: eiπ=11=1.e^{-i\pi} = \dfrac{1}{-1} = -1 . Step 3: Equating both equations in the above two steps gives eiπ=eiπ. \large e^{i \pi} = e^{-i \pi} . Step 4: Since the bases are the same, iπ=iπ. i \pi = -i \pi . Step 5: Canceling the imaginary number yields π=π. \pi = -\pi .

×

Problem Loading...

Note Loading...

Set Loading...