document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205743>Question 205743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all solutions of the equation z^2 = -6 + 8i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155367 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=155367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find all solutions of the equation z^2 = -6 + 8i<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "z = sqrt(-6 + 8i)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Convert to trig form:<BR>\n" );
document.write( "r = sqrt(6^2+8^2) = 10<BR>\n" );
document.write( "theta = arctan(8/-6) = -53.13;<BR>\n" );
document.write( "But z^2 is in the 2nd quadrant so theta = -53.13+180 = 126.87<BR>\n" );
document.write( "-----------------------------------------------<BR>\n" );
document.write( "z = sqrt(10)(cis(126.87+360n)/2)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "let n = 0, then z = sqrt(10)(cis(63.435))<BR>\n" );
document.write( "---<BR>\n" );
document.write( "let n = 1, then z = sqrt(10)(cis(243.435)<BR>\n" );
document.write( "======<BR>\n" );
document.write( "In Rectangular form<BR>\n" );
document.write( "For n=0<BR>\n" );
document.write( "x = sqrt(10)cos(63.435) = 1.414 or sqrt(2)<BR>\n" );
document.write( "y = sqrt(10)sin(63.435) = 2.828<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "For n = 1<BR>\n" );
document.write( "x = sqrt(10)cos(243.435) = -sqrt(2)<BR>\n" );
document.write( "y = sqrt(10)sin(243.435) = -2.828...<BR>\n" );
document.write( "=====================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );