document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184217>Question 1184217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28z-1%29%2F%28z%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28z-1%29%2F%28z%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is purely imaginary then what is value of |z|? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814744 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28z-1%29%2F%28z%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28z-1%29%2F%28z%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is purely imaginary, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28z-1%29%2F%28z%2B1%29+=+Ai ALIGN=MIDDLE  ALT=\"+%28z-1%29%2F%28z%2B1%29+=+Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%3C%3E0 ALIGN=MIDDLE  ALT=\"A%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Let z = a + bi.<BR>\n" );
document.write( "===> z - 1 = A(z+1)i  ===> a + bi - 1 = A(a + bi + 1)i\r<BR>\n" );
document.write( "\n" );
document.write( "===> a + bi - 1 = A((a + 1)i - b) = A(a+1)i - Ab\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<===> (a - 1 + Ab) + (b - A(a+1))i = 0\r<BR>\n" );
document.write( "\n" );
document.write( "===> a - 1 + Ab = 0  and b - A(a+1) = 0, or \r<BR>\n" );
document.write( "\n" );
document.write( "===> a + Ab = 1 and -Aa + b = A.\r<BR>\n" );
document.write( "\n" );
document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%281-A%5E2%29%2F%281%2BA%5E2%29 ALIGN=MIDDLE  ALT=\"a+=+%281-A%5E2%29%2F%281%2BA%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+%282A%29%2F%281%2BA%5E2%29 ALIGN=MIDDLE  ALT=\"b+=+%282A%29%2F%281%2BA%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > after solving the system for a and b.\r<BR>\n" );
document.write( "\n" );
document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z++=+a%2Bbi+=++%281-A%5E2%29%2F%281%2BA%5E2%29+%2B+i%2A%28%282A%29%2F%281%2BA%5E2%29%29 ALIGN=MIDDLE  ALT=\"z++=+a%2Bbi+=++%281-A%5E2%29%2F%281%2BA%5E2%29+%2B+i%2A%28%282A%29%2F%281%2BA%5E2%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=abs%28z%29+=+sqrt%28+%28%281-A%5E2%29%2F%281%2BA%5E2%29%29%5E2+%2B+%28%282A%29%2F%281%2BA%5E2%29%29%5E2%29 ALIGN=MIDDLE   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=sqrt%28+%28%281-2A%5E2+%2B+A%5E4%29%2F%281%2BA%5E2%29%5E2+%2B+%284A%5E2%29%2F%281%2BA%5E2%29%5E2%29%29+=+sqrt+%28%281%2B2A%5E2+%2B+A%5E4%29%2F%281%2BA%5E2%29%5E2+%29+=+1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28abs%28z%29+=+1%29 ALIGN=MIDDLE  ALT=\"highlight%28abs%28z%29+=+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );