document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174537>Question 1174537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the square roots of the complex number. (Enter your answers as a comma-separated list.)\r<BR>\n" );
document.write( "\n" );
document.write( "13i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799963 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13i+=+13%2Acis%28pi%2F2%29 ALIGN=MIDDLE  ALT=\"13i+=+13%2Acis%28pi%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "By deMoivre's Theorem, the primary square root is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813i%29+=+sqrt%2813%29%2Acis%28%28pi%2F2%29%2F2%29+=+sqrt%2813%29%2Acis%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%2813i%29+=+sqrt%2813%29%2Acis%28%28pi%2F2%29%2F2%29+=+sqrt%2813%29%2Acis%28pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The n n-th roots of a complex number have the same magnitude, and they are separated in the complex plane by angles of (2pi)/n.<br><BR>\n" );
document.write( "For this problem with square roots, the other square root is (2pi)/2 = pi radians past the primary square root: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813%29%2Acis%285pi%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%2813%29%2Acis%285pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813%29%2Acis%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%2813%29%2Acis%28pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813%29%2Acis%285pi%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%2813%29%2Acis%285pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );