document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=766639>Question 766639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1-4i)ˆ2 + 3 + (8i) - (-2-7i) how do I simplify this? Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467097 by </B><A HREF=/tutors/aboutme.mpl?userid=Shana-D77><B>Shana-D77(132)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Shana-D77><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=Shana-D77><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=467097\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the hardest part is simplifying (1-4i)ˆ2:<BR>\n" );
document.write( "Let's first remember...<BR>\n" );
document.write( "i = sqrt(-1)<BR>\n" );
document.write( "i^2 = -1<BR>\n" );
document.write( "i^3 = -(sqrt(-1))<BR>\n" );
document.write( "i^4 = 1<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "(1-4i)ˆ2 = (1-4i)(1-4i) = 1 - 4i - 4i + 16i^2<BR>\n" );
document.write( "Since i^2 = -1, the above simplifies to: 1 - 8i - 16 <BR>\n" );
document.write( "Which simplifies to: -15 - 8i<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Now add in the rest of the problem:<BR>\n" );
document.write( "-15 - 8i + 3 + (8i) - (-2-7i)<BR>\n" );
document.write( "-15 - 8i + 3 + 8i + 2 + 7i (distributed the - outside (-2-7i))<BR>\n" );
document.write( "-10 + 7i (combined like terms) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );