document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162768>Question 1162768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find real numbers a and b such that (𝑎 + 𝑏i)^2<BR>\n" );
document.write( "= −3 − 4i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786619 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=786619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find real numbers a and b such that (𝑎 + 𝑏i)^2<BR>\n" );
document.write( "= −3 − 4i<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "a^2 + 2abi - b^2 = -3 - 4i<BR>\n" );
document.write( "a^2 - b^2 = -3<BR>\n" );
document.write( "2ab = -4<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "b^2 - a^2 = 3<BR>\n" );
document.write( "b = -2/a<BR>\n" );
document.write( "---<BR>\n" );
document.write( "4/a^2 - a^2 = 3<BR>\n" );
document.write( "4 - a^4 = 3a^2<BR>\n" );
document.write( "a^4 + 3a^2 - 4 = 0<BR>\n" );
document.write( "(a^2 + 4)*(a^2 - 1) = 0<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = -2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "(1 - 2i)*(1 - 2i) = 1 -4 - 4i = -3 - 4i<BR>\n" );
document.write( "===========<BR>\n" );
document.write( "a = -1<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( "=================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );