Does $180i = \pi(i)$ through euler's identity by $e^{90i} = 0 + i$

Question

I have a strange question: If $e^{ix} = cosx + isinx$ then shouldn't $e^{90i} = cos90 + isin90$ Which should simplify to $e^{90i} = 0 + i$ making $e^{90i} = i$ But we already know that $e^{\pi i} = i^{2}$ so doesn't $e^{2\cdot90i} =e^{\pi i}$ which should mean $180i=\pi i$. did i miss something or am i stressing over something unimportant?

Answer 1

The thing you are forgetting is that degrees are a unit. Radians are measured unitless. Therefore, we always need to specify the degree symbol. So yes, if we add the degree symbols, the statements are correct.