document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394194>Question 394194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello. My son is struggling with complex numbers and this stuff is like a second language to me. Any help is greatly appreciated. Thanks.\r<BR>\n" );
document.write( "\n" );
document.write( "1) 4i^5-6i^4+3i^3-9i^2\r<BR>\n" );
document.write( "\n" );
document.write( "2) 3i^4-(2i-6)-5i^2+(2+12i)\r<BR>\n" );
document.write( "\n" );
document.write( "3) (4i-5)*(5i-4)\r<BR>\n" );
document.write( "\n" );
document.write( "4) (5i+8)/(3i)\r<BR>\n" );
document.write( "\n" );
document.write( "5) (11-3i)/(4+5i) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279691 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4i%5E5-6i%5E4%2B3i%5E3-9i%5E2+ ALIGN=MIDDLE  ALT=\"4i%5E5-6i%5E4%2B3i%5E3-9i%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28i%5E2%29%28i%5E2%29%28i%29+-+6%28i%5E2%29%28i%5E2%29+%2B+3%28i%5E2%29%28i%29+-+9%28i%5E2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28i%5E2%29=-1 ALIGN=MIDDLE  ALT=\"%28i%5E2%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-1%29%28-1%29%28i%29+-+6%28-1%29%28-1%29+%2B+3%28-1%29%28i%29+-+9%28-1%29+ ALIGN=MIDDLE  ALT=\"4%28-1%29%28-1%29%28i%29+-+6%28-1%29%28-1%29+%2B+3%28-1%29%28i%29+-+9%28-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4i+-+6+-+3i+%2B+9+ ALIGN=MIDDLE  ALT=\"4i+-+6+-+3i+%2B+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+%2B+3+ ALIGN=MIDDLE  ALT=\"i+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3i%5E4-%282i-6%29-5i%5E2%2B%282%2B12i%29+ ALIGN=MIDDLE  ALT=\"3i%5E4-%282i-6%29-5i%5E2%2B%282%2B12i%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28i%5E2%29%28i%5E2%29-+2i+%2B+6+-5i%5E2+%2B2+%2B12i ALIGN=MIDDLE  ALT=\"3%28i%5E2%29%28i%5E2%29-+2i+%2B+6+-5i%5E2+%2B2+%2B12i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-1%29%28-1%29-+2i+%2B+6+-5%28-1%29+%2B+2+%2B12i ALIGN=MIDDLE  ALT=\"3%28-1%29%28-1%29-+2i+%2B+6+-5%28-1%29+%2B+2+%2B12i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+-+2i+%2B+6+%2B5+%2B+2+%2B12i ALIGN=MIDDLE  ALT=\"3+-+2i+%2B+6+%2B5+%2B+2+%2B12i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+%2B10i+ ALIGN=MIDDLE  ALT=\"+16+%2B10i+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284i-5%29%2A%285i-4%29+ ALIGN=MIDDLE  ALT=\"+%284i-5%29%2A%285i-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....multiply\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%284i%29%285i%29+-%284i%29%284%29+-5%285i%29+%2B+5%2A4%29 ALIGN=MIDDLE  ALT=\"+%28%284i%29%285i%29+-%284i%29%284%29+-5%285i%29+%2B+5%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%2820i%5E2%29+-%2816i%29+-25i+%2B+20%29 ALIGN=MIDDLE  ALT=\"+%28%2820i%5E2%29+-%2816i%29+-25i+%2B+20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%2820%28-1%29%29+-16i+-25i+%2B+20%29 ALIGN=MIDDLE  ALT=\"+%28%2820%28-1%29%29+-16i+-25i+%2B+20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cross%28-20%29+-16i+-25i+%2Bcross%28+20%29%29 ALIGN=MIDDLE  ALT=\"+cross%28-20%29+-16i+-25i+%2Bcross%28+20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16i+-25i%29 ALIGN=MIDDLE  ALT=\"+-16i+-25i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-41i%29 ALIGN=MIDDLE  ALT=\"+-41i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285i%2B8%29%2F%283i%29 ALIGN=MIDDLE  ALT=\"%285i%2B8%29%2F%283i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285i%2B8%29%2F%283i%29 ALIGN=MIDDLE  ALT=\"%285i%2B8%29%2F%283i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3i ALIGN=MIDDLE  ALT=\"3i\"   DISABLED_style= \"max-width:90%; height:auto;\" > to eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > from denominator\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285i%2B8%29%283i%29%2F%283i%29%283i%29 ALIGN=MIDDLE  ALT=\"%285i%2B8%29%283i%29%2F%283i%29%283i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285i%2B8%29%283i%29%2F%289i%5E2%29 ALIGN=MIDDLE  ALT=\"%285i%2B8%29%283i%29%2F%289i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815i%5E2%2B24i%29%2F%289%2A-1%29 ALIGN=MIDDLE  ALT=\"%2815i%5E2%2B24i%29%2F%289%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%28-1%29%2B24i%29%2F%28-9%29 ALIGN=MIDDLE  ALT=\"%2815%28-1%29%2B24i%29%2F%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%2815-24i%29%29%2F-9 ALIGN=MIDDLE  ALT=\"%28-%2815-24i%29%29%2F-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815-24i%29%2F9 ALIGN=MIDDLE  ALT=\"%2815-24i%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811-3i%29%2F%284%2B5i%29 ALIGN=MIDDLE  ALT=\"%2811-3i%29%2F%284%2B5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811-3i%29%2F%284%2B5i%29 ALIGN=MIDDLE  ALT=\"%2811-3i%29%2F%284%2B5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811-3i%29%284-5i%29+%2F%284%2B5i%29%284-5i%29 ALIGN=MIDDLE  ALT=\"%2811-3i%29%284-5i%29+%2F%284%2B5i%29%284-5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2844+-+55i+-12i+%2B15i%5E2%29%2F%2814+-+20i+%2B+20i+-+25i%5E2%29 ALIGN=MIDDLE  ALT=\"%2844+-+55i+-12i+%2B15i%5E2%29%2F%2814+-+20i+%2B+20i+-+25i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2844+-+67i+%2B15%28-1%29%29%2F%2814+-+25%28-1%29%29 ALIGN=MIDDLE  ALT=\"%2844+-+67i+%2B15%28-1%29%29%2F%2814+-+25%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2844+-+67i+-15%29%2F%2814+%2B25%29 ALIGN=MIDDLE  ALT=\"%2844+-+67i+-15%29%2F%2814+%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829+-+67i+%29%2F39 ALIGN=MIDDLE  ALT=\"%2829+-+67i+%29%2F39\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );