<p>Hi, I've heard that e^(pi)(i)=1</p>
<p>Is this true, and if so can someone please explain it to me?</p>
<p>thanks!</p>
<p>e^iπ=-1 actually.</p>
<p>It involves calculus. Basically you take the Taylor series for sinx and cosx, and you get the equation e^ix=cosx+isinx. Substitute π for x and there you go.</p>
<p>^It’s a really sweet derivation, actually. One of my favorites, due to its linking of a lot of areas of mathematics and it’s inherent simplicity. When going through Taylor series (or cis functions, which will probably be later) definitely ask your teacher to derive it, if they didn’t do it at first.</p>
<p>And the expression: e^(pi)(i)+1=0 has five very significant mathematical numbers (probably the most significant five, when you think about it). Who knew math could be so cool!?</p>
<p>Thank you guys so much. :)</p>
<p>yeah, math IS cool</p>