document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=423089>Question 423089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all seventh roots of 3+4i please try and give all steps... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #295199 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=295199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find all seventh roots of 3+4i please try and give all steps...<BR>\n" );
document.write( "----<BR>\n" );
document.write( "r = sqrt(3^2+4^2) = 5<BR>\n" );
document.write( "theta = tan^-1(4/3) = 53.13 degrees<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "(3+4i)^(1/7) = 5^(1/7)(cis(53.13+360n)/7)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "To find the 7 roots let n = 0,1,2,3,...,6<BR>\n" );
document.write( "Note: 360/7 = 51.43 degrees<BR>\n" );
document.write( "and 53.13/7 = 7.59<BR>\n" );
document.write( "---<BR>\n" );
document.write( "So for n = 3 you get: 5^(1/7)cis(7.59+3(41.43))<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "-------------------------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );