document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246256>Question 246256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the complex number z = a + bi such that z^3= 2 + 2i where a is less than or equal to 0 and b is greater than or equal to 0.\r<BR>\n" );
document.write( "\n" );
document.write( "I really don't know how to approach this question but I'm guessing you have to use the definition (a + bi)(c + di) = (ac-bd)+(ad+bc)i? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179881 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=179881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hint: Convert the complex number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B2i ALIGN=MIDDLE  ALT=\"2%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > into polar form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=r%28cos%28x%29%2Bi%2Asin%28x%29%29 ALIGN=MIDDLE  ALT=\"z=r%28cos%28x%29%2Bi%2Asin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where 'r' is the magnitude and 'x' is the angle. From there, use a variation of <a  rel=nofollow HREF=\"http://en.wikipedia.org/wiki/De_Moivre%27s_formula#Applications\">De Moivre's Theorem</a>. Let me know if this helps or not. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );