document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156361>Question 1156361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch the set of complex numbers that satisfy |z|=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779060 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=779060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "For any complex number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+a%2Bbi ALIGN=MIDDLE  ALT=\"z+=+a%2Bbi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the magnitude of the complex number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29+=+sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"abs%28z%29+=+sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can see this through finding the distance from (0,0) to (a,b). This is effectively the same as using the pythagorean theorem.\r<BR>\n" );
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document.write( "We want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28z%29+=+1 ALIGN=MIDDLE  ALT=\"abs%28z%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%2Bb%5E2%29+=+1 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%2Bb%5E2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+=+1 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > when we square both sides. Note how (a,b) = (x,y), so we go from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+=+1 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2By%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%5E2%2By%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a circle with radius 1 and center (0,0). Compare this to the general form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The diagram will be an empty (or not filled in) circle because we're only considering points on the circle itself. \r<BR>\n" );
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document.write( "Similar problem:<BR>\n" );
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