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 \(e^{2i}=1\).
by
Lee Dongheng