document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=385329>Question 385329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the 3 complex solutions to the equation z^3 + 2i = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #272648 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=272648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the 3 complex solutions to the equation z^3 + 2i = 0<BR>\n" );
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document.write( "z^3 = -2i<BR>\n" );
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document.write( "Since i^2 = -1<BR>\n" );
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document.write( "z^3 = 2i^3<BR>\n" );
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document.write( "z^3-(cbrt(2)i)^3 = 0<BR>\n" );
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document.write( "Factor:<BR>\n" );
document.write( "(z-(cbrt(2)i)(z^2+(cbrt(2)i)+(cbrt(2)i)^2)=0<BR>\n" );
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document.write( "z = cbrt(2)i plus two solution from the quadratic factor.<BR>\n" );
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document.write( "I'll leave the quadratic to you.<BR>\n" );
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document.write( "You could also work this problem by converting to polar form.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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