document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084358>Question 1084358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (cosx - isinx)^5<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 #698466 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=698466\">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=+a+%2B+b%2Ai++=+r%2Acos%28theta%29+%2B+i%2Ar%2Asin%28theta%29+=++r%2Ae%5E%28i%2Atheta%29+ ALIGN=MIDDLE  ALT=\"+a+%2B+b%2Ai++=+r%2Acos%28theta%29+%2B+i%2Ar%2Asin%28theta%29+=++r%2Ae%5E%28i%2Atheta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where  <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+sqrt%28a%5E2%2Bb%5E2%29+ ALIGN=MIDDLE  ALT=\"+r+=+sqrt%28a%5E2%2Bb%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+=+tan%28-1%29%28b%2Fa%29+ ALIGN=MIDDLE  ALT=\"+theta+=+tan%28-1%29%28b%2Fa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+sqrt%28+%28cos%28x%29%29%5E2+%2B+%28-sin%28x%29%29%5E2++%29+++=+sqrt%28+cos%5E2%28x%29+%2B+sin%5E2%28x%29+%29+=+sqrt%281%29+=+1+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+=+tan%5E-1%28-sin%28x%29+%2F+cos%28x%29%29+=+tan%5E-1%28-tan%28x%29%29+=+-x+ ALIGN=MIDDLE  ALT=\"+theta+=+tan%5E-1%28-sin%28x%29+%2F+cos%28x%29%29+=+tan%5E-1%28-tan%28x%29%29+=+-x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28cos%28x%29%2Bi%2Asin%28x%29%29%5E5+=+%28e%5E%28-i%2Ax%29%29%5E5+=+e%5E%28i%2A-5x%29+=+cos%28-5x%29+%2B+i%2Asin%28-5x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28-theta%29+=+cos%28theta%29+ ALIGN=MIDDLE  ALT=\"+cos%28-theta%29+=+cos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28-theta%29+=+-sin%28theta%29+ ALIGN=MIDDLE  ALT=\"+sin%28-theta%29+=+-sin%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0%3C=theta%3C=pi+ ALIGN=MIDDLE  ALT=\"+0%3C=theta%3C=pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "lets us simplify to:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28cos%285x%29+-+i%2Asin%285x%29%29+ ALIGN=MIDDLE  ALT=\"+highlight%28cos%285x%29+-+i%2Asin%285x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );