document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=245751>Question 245751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the zeros of f(x)=x^2+2ix-3.<BR>\n" );
document.write( "I tried using the quadratic equation, but the i is confusing me.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179460 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=179460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Just treat this quadratic as you normally would, but make sure to follow the rules of complex arithmetic.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2ix-3=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2ix-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2ix-3 ALIGN=MIDDLE  ALT=\"x%5E2%2B2ix-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1 ALIGN=MIDDLE  ALT=\"A=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=2i ALIGN=MIDDLE  ALT=\"B=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-3 ALIGN=MIDDLE  ALT=\"C=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"x\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%282i%29+%2B-+sqrt%28+%282i%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%282i%29+%2B-+sqrt%28+%282i%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1 ALIGN=MIDDLE  ALT=\"A=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=2i ALIGN=MIDDLE  ALT=\"B=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-3 ALIGN=MIDDLE  ALT=\"C=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2i+%2B-+sqrt%28+-4-4%281%29%28-3%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2i+%2B-+sqrt%28+-4-4%281%29%28-3%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2i ALIGN=MIDDLE  ALT=\"2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%5E2=%282i%29%282i%29=4i%5E2=4%28-1%29=-4 ALIGN=MIDDLE  ALT=\"%282i%29%5E2=%282i%29%282i%29=4i%5E2=4%28-1%29=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=%28sqrt%28-1%29%29%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=%28sqrt%28-1%29%29%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2i+%2B-+sqrt%28+-4%2B12+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2i+%2B-+sqrt%28+-4%2B12+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4, 1 and -3 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%281%29%28-3%29=12 ALIGN=MIDDLE  ALT=\"-4%281%29%28-3%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2i+%2B-+sqrt%28+-4%2B12+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2i+%2B-+sqrt%28+-4%2B12+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2i+%2B-+sqrt%28+8+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2i+%2B-+sqrt%28+8+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2i+%2B-+2%2Asqrt%28+2+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2i+%2B-+2%2Asqrt%28+2+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i+%2B-+sqrt%28+2+%29 ALIGN=MIDDLE  ALT=\"x+=+-i+%2B-+sqrt%28+2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i+%2B+sqrt%28+2+%29 ALIGN=MIDDLE  ALT=\"x+=+-i+%2B+sqrt%28+2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i+-+sqrt%28+2+%29 ALIGN=MIDDLE  ALT=\"x+=+-i+-+sqrt%28+2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the 'plus/minus'\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i+%2B+sqrt%28+2+%29 ALIGN=MIDDLE  ALT=\"x+=+-i+%2B+sqrt%28+2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i+-+sqrt%28+2+%29 ALIGN=MIDDLE  ALT=\"x+=+-i+-+sqrt%28+2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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