Can you spot that mistake?

Algebra Level 2

Dexter, a math lover, claims that he has proven e2i=1e^{2i}=1, but applying the Euler's formula eix=cosx+isinxe^{ix}=\cos x + i \sin x, e2ie^{2i} is actually a complex number. In which of these steps does he first make a mistake?

Step 1: As we know, eiπ=1e^{i\pi}=-1.
Step 2: Squaring both sides, we get (eiπ)2=1\big(e^{i\pi}\big)^2=1.
Step 3: Exchanging the exponents, (e2i)π=1\big(e^{2i}\big)^\pi=1.
Step 4: Multiplying 1π\frac{1}{\pi} at the exponents of both sides, we claim that e2i=1e^{2i}=1.


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