document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=431413>Question 431413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Why does e<sup>i*pi</sup>+1=0 other than the fact that my calculator says so, and so I believe it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299519 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=299519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Apparently it seems like the other tutor taught you this...:)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From Euler's formula, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28i%2Atheta%29+=+cos%28theta%29+%2B+i%2Asin%28theta%29 ALIGN=MIDDLE  ALT=\"e%5E%28i%2Atheta%29+=+cos%28theta%29+%2B+i%2Asin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. By substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+pi ALIGN=MIDDLE  ALT=\"theta+=+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > you will obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28i%2Api%29+=+-1 ALIGN=MIDDLE  ALT=\"e%5E%28i%2Api%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28i%2Api%29+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"e%5E%28i%2Api%29+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Euler's formula itself is derived using the Maclaurin series for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex+=+sum%28%28x%5Ek%29%2Fk%21%2C+k=0%2C+infinity%29 ALIGN=MIDDLE  ALT=\"e%5Ex+=+sum%28%28x%5Ek%29%2Fk%21%2C+k=0%2C+infinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (you will learn this sometime in calculus). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );