document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198297>Question 1198297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (x +iy)^9 - (ix+y)^9 = 2i, find the value of x, y ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832235 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=832235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I'm posting this response to try to get input from other tutors....<br><BR>\n" );
document.write( "It seems to me that there will be no solution to the given equation.  I will be interested in anything useful that others have regarding this problem.<br><BR>\n" );
document.write( "Below are my thoughts about the problem that lead me to my conclusion that there is no solution.<br><BR>\n" );
document.write( "Represented in polar form, x+iy and y+ix have equal magnitudes and are symmetrical about the line y=x.<br><BR>\n" );
document.write( "The angles associated with the two complex numbers can then be represented as (45+a) and (45-a) degrees.<br><BR>\n" );
document.write( "But applying deMoivre's Theorem to the given expression shows that no value of a will produce a value for the given expression with an angle of 90 degrees -- as required by the given expression being equal to 2i.<br><BR>\n" );
document.write( "Experimenting with random values of a on wolframalpha.com in fact shows that any value of a produces a result in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%281-i%29 ALIGN=MIDDLE  ALT=\"c%281-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where c is a real number.<br><BR>\n" );
document.write( "Any comments...?<br><BR>\n" );
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