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## Main Question or Discussion Point

I have a couple questions regarding Euler's formula. First I'm confused about the notation e

^{i[tex]\vartheta[/tex]}. To me the notation implies that we are raising e to the exponent*i*multiplied by [tex]\vartheta[/tex]. Is this correct? If so, how would you do that? Also, my second question regards the second part of that equation: cos[tex]\vartheta[/tex] +*i*sin[tex]\vartheta[/tex]. That makes sense to me, but sometimes I see it written as cosx +*i*sinx. I don't understand what that means. What would be the cosine or sine of x?
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