document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550679>Question 550679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify <BR>\n" );
document.write( "2i + 5<BR>\n" );
document.write( "______<BR>\n" );
document.write( "   <BR>\n" );
document.write( "3i - 4\r<BR>\n" );
document.write( "\n" );
document.write( "to the form ai + b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Express z = -2 -5i  in polar form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Express z = 3 + 5i in exponential form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use De Moivre's Theorem to express cos4 0  as powers of cos0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359173 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=359173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplify <BR>\n" );
document.write( "2i + 5<BR>\n" );
document.write( "______<BR>\n" );
document.write( "   <BR>\n" );
document.write( "3i - 4\r<BR>\n" );
document.write( "\n" );
document.write( "to the form ai + b.<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(2i + 5)/(3i - 4)<BR>\n" );
document.write( "Multiply by the conjugate of the DEN<BR>\n" );
document.write( "= (2i + 5)*(3i + 4)/((3i - 4)*3i + 4))<BR>\n" );
document.write( "= (6i^2 + 20 + 23i) / (9i^2 - 16)<BR>\n" );
document.write( "= (-6 + 20 + 23i) / (-9 - 16)<BR>\n" );
document.write( "= (14 + 23i)/(-25)<BR>\n" );
document.write( "= (-14/25) - (23/25)i<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Express z = -2 -5i  in polar form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%282%5E2+%2B+5%5E2%29+=+sqrt%2829%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%282%5E2+%2B+5%5E2%29+=+sqrt%2829%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Angle = arctan(-2/-5) = arctan(0.4)<BR>\n" );
document.write( "Angle =~ 21.8 degs in Q3 --> 201.8 degs = 3.522 radians<BR>\n" );
document.write( "--> (sqrt(29),3.522)<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Express z = 3 + 5i in exponential form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use De Moivre's Theorem to express cos4 0  as powers of cos0. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );