document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075983>Question 1075983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can somebody fill me in a bit on Euler’s formula?\r<BR>\n" );
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document.write( "e^(a + bi) = e^a*(cos b + i sin b) -- Euler's Formula.\r<BR>\n" );
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document.write( "His equation gives rise to e^(&#960;i) + 1 = 0. \r<BR>\n" );
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document.write( "'0, 1,&#960; , e, and i' Are all in one equation. \r<BR>\n" );
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document.write( "Could you explain how Euler’s formula could be applied to derive this equation? Thank you very much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690682 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=690682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28a%2Bbi%29+=+%28e%5Ea%29%2A%28e%5E%28bi%29%29+=+%28e%5Ea%29%2A%28cos%28b%29+%2B+i%2Asin%28b%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let a=0 so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ea+=+e%5E0+=+1 ALIGN=MIDDLE  ALT=\"e%5Ea+=+e%5E0+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=pi ALIGN=MIDDLE  ALT=\"b=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28bi%29+=+e%5E%28%28pi%29i%29+=+cos%28pi%29+%2B+i%2Asin%28pi%29+=+-1+%2B+0%2Ai+=+-1+ ALIGN=MIDDLE  ALT=\"e%5E%28bi%29+=+e%5E%28%28pi%29i%29+=+cos%28pi%29+%2B+i%2Asin%28pi%29+=+-1+%2B+0%2Ai+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Put the two together and the  result is the famous Euler's Identity:   <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28%28pi%29i%29+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"e%5E%28%28pi%29i%29+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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