document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175558>Question 175558</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618250204/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the Absolute Value of a complex number?<BR>\n" );
document.write( "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 #130647 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=130647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The absolute value of any complex number in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bbi ALIGN=MIDDLE  ALT=\"a%2Bbi\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28a%2Bbi%29=sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28a%2Bbi%29=sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Remember, absolute value geometrically is the distance from the origin. So in this case, we're finding the distance is from the point (a,b) to the origin (0,0) (in the complex plane)\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "Problem:\r<BR>\n" );
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document.write( "Find the absolute value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-6i ALIGN=MIDDLE  ALT=\"3-6i\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Solution:\r<BR>\n" );
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document.write( "In this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   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=abs%28a%2Bbi%29=sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28a%2Bbi%29=sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283-6i%29=sqrt%28%283%29%5E2%2B%28-6%29%5E2%29 ALIGN=MIDDLE  ALT=\"abs%283-6i%29=sqrt%28%283%29%5E2%2B%28-6%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   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=abs%283-6i%29=sqrt%289%2B36%29 ALIGN=MIDDLE  ALT=\"abs%283-6i%29=sqrt%289%2B36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 3 to get 9. Square -6 to get 36\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283-6i%29=sqrt%2845%29 ALIGN=MIDDLE  ALT=\"abs%283-6i%29=sqrt%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283-6i%29=3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"abs%283-6i%29=3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "So the absolute value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-6i ALIGN=MIDDLE  ALT=\"3-6i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.708 ALIGN=MIDDLE  ALT=\"6.708\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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