document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40889>Question 40889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is one of the so called examples in my book <BR>\n" );
document.write( "Simplify in euler form: (1-i)^5 (sqrt3+i)^3<BR>\n" );
document.write( "How is it possible to get to this?<BR>\n" );
document.write( "(sqrt2 e(-ipi/4))^5 (2e(ipi/6)^3. <BR>\n" );
document.write( "And from there is simplifies down to -32-32i, that I am ok with but why is it no one can explain the first step? Smoke and mirrors?<BR>\n" );
document.write( "And in all examples they conveniently use (1-i) but what about any other numbers?<BR>\n" );
document.write( "Surely someone must know how to explain this?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27914 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well since you can express<BR>\n" );
document.write( "e^iq = cos q + i*sin q<BR>\n" );
document.write( "you can express<BR>\n" );
document.write( "(sqrt(2)*e(-ipi/4)) as<BR>\n" );
document.write( "(sqrt(2))(cos (-pi/4) + i*sin(-pi/4)) which becomes, after evaluating the trig values,<BR>\n" );
document.write( "1 - i<BR>\n" );
document.write( "And then, by the same method 2e(ipi/6) becomes sqrt(3)+i...<BR>\n" );
document.write( "Your book does not seem to be too instructive on how to go backwards however... </SPAN>\n" );
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