# Can you spot that mistake?

Algebra Level 2

Dexter, a math lover, claims that he has proven $$e^{2i}=1$$, but applying the Euler's formula $$e^{ix}=\cos x + i \sin x$$, $$e^{2i}$$ is actually a complex number. In which of these steps does he first make a mistake?

Step 1: As we know, $$e^{i\pi}=-1$$.
Step 2: Squaring both sides, we get $$\big(e^{i\pi}\big)^2=1$$.
Step 3: Exchanging the exponents, $$\big(e^{2i}\big)^\pi=1$$.
Step 4: Multiplying $$\frac{1}{\pi}$$ at the exponents of both sides, we claim that $$e^{2i}=1$$.

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