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" );
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document.write( "1) 4i^5-6i^4+3i^3-9i^2\r<BR>\n" );
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document.write( "2) 3i^4-(2i-6)-5i^2+(2+12i)\r<BR>\n" );
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document.write( "3) (4i-5)*(5i-4)\r<BR>\n" );
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document.write( "4) (5i+8)/(3i)\r<BR>\n" );
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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 #279683 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=279683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note:<BR>\n" );
document.write( "i = i<BR>\n" );
document.write( "i^2 = -1<BR>\n" );
document.write( "i^3 = -i<BR>\n" );
document.write( "i^4 = 1<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "1) 4i^5-6i^4+3i^3-9i^2<BR>\n" );
document.write( "= 4i - 6*1+3(-i)-9(-1)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= -6+9+4i-3i<BR>\n" );
document.write( "= 3+i<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "2) 3i^4-(2i-6)-5i^2+(2+12i)<BR>\n" );
document.write( "= 3-2i+6-5(-1)+2+12i<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= 3+6+4+2 -2i+12i<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= 15+10i<BR>\n" );
document.write( "----------------------------\r<BR>\n" );
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document.write( "3) (4i-5)*(5i-4) <BR>\n" );
document.write( "= 20i^2-16i-25i+20<BR>\n" );
document.write( "= -20+20-41i<BR>\n" );
document.write( "= -41i<BR>\n" );
document.write( "--------------------------------- <BR>\n" );
document.write( "4) (5i+8)/(3i)<BR>\n" );
document.write( "= [(-3i)(5i+8)]/[(-3i)(3i)]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [15-24i]/9<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [5-8i]/3<BR>\n" );
document.write( "--------------------------------- <BR>\n" );
document.write( "5) (11-3i)/(4+5i)<BR>\n" );
document.write( "= [(11-3i)(4-5i)]/[(4+5i)(4-5i)]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [44-55i-12i-15]/[16+25]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [29-67i]/41<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );