I have a couple questions regarding Euler's formula. First I'm confused about the notation ei[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] + isin[tex]\vartheta[/tex]. That makes sense to me, but sometimes I see it written as cosx + isinx. I don't understand what that means. What would be the cosine or sine of x?