Friday, 15 April 2016

complex analysis - Why is sinx the imaginary part of eix?

Most of us who are studying mathematics are familiar with the famous eix=cos(x)+isin(x). Why is it that we have eix=cos(x)+isin(x) and not eix=sin(x)+icos(x)? I haven't studied Complex Analysis to know the answer to this question. It pops up in Linear Algebra, Differential Equations, Multivariable Equations and many other fields. But I feel like textbooks and teachers just expect us students to take it as given without explaining it to a certain extent. I also couldn't find any good article that explains this.

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real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...