Paradox observed while studying Euler's formula

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I am a first-year uni student. While messing around with Euler's formula I got this paradox $$e^{i\theta}=(e^{i2\pi})^{\frac{\theta}{2\pi}}=(\cos(2\pi) + i \sin(2\pi))^{\frac{\theta}{2\pi}}=1$$ I asked my university tutor and he didn't know the answer either. How can I explain this?