document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389436>Question 389436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HOW TO DETERMINE i2=&#8722;1 FROM THE EULER`S EQUATION USING LOGARITHM/WITHOUT LOGARITHM? PLEASE TELL ME IN DETAILS.     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275959 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=275959\">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=i%5E2+=+-1 ALIGN=MIDDLE  ALT=\"i%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > by definition. Or, we use Euler's formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Eix+=+cis+x+=+cos+x+%2B+i+sin+x ALIGN=MIDDLE  ALT=\"e%5Eix+=+cis+x+=+cos+x+%2B+i+sin+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Letting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+pi%2F2 ALIGN=MIDDLE  ALT=\"x+=+pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ei%28pi%2F2%29+=+cos+%28pi%2F2%29+%2B+i+sin+%28pi%2F2%29+=+i ALIGN=MIDDLE  ALT=\"e%5Ei%28pi%2F2%29+=+cos+%28pi%2F2%29+%2B+i+sin+%28pi%2F2%29+=+i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Squaring both sides,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ei%28pi%29+=+cos+%28pi%29+%2B+i+sin+%28pi%29+=+-1 ALIGN=MIDDLE  ALT=\"e%5Ei%28pi%29+=+cos+%28pi%29+%2B+i+sin+%28pi%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This implies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2+=+-1 ALIGN=MIDDLE  ALT=\"i%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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