document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206092>Question 1206092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given that z1=2+i and z2=-3+4i and 1/z3=1/z1+1/z2. determine the value of z3 in standard form.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843301 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given that z1=2+i and z2=-3+4i and 1/z3=1/z1+1/z2. determine the value of z3 in standard form.\r<BR>\n" );
document.write( "\n" );
document.write( "z1=2+i \r<BR>\n" );
document.write( "\n" );
document.write( " z2=-3+4i\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fz1+=+%281%2F%282%2Bi%29%29%2A%28%282-i%29%2F%282-i%29%29=+%282-i%29%2F%28%284-i%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-i%29%2F5 ALIGN=MIDDLE  ALT=\"%282-i%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >   ............ (i^2=-i)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fz2+=+%281%2F%28-3%2B4i%29%29%2A%28%28-3-4i%29%2F%28-3-4i%29%29=+%28-3-4i%29%2F%28%289-16i%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3-4i%29%2F25 ALIGN=MIDDLE  ALT=\"%28-3-4i%29%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >   ............ (i^2=-i)<BR>\n" );
document.write( "(<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2Fz3%29+=+%28+%282-i%29%2F5+%29%2B+%28%28-3-4i%29%2F25%29 ALIGN=MIDDLE  ALT=\"+%281%2Fz3%29+=+%28+%282-i%29%2F5+%29%2B+%28%28-3-4i%29%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Add take LCM\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fz3+=++%2810-5i+%2B-3-4i%29%2F25 ALIGN=MIDDLE  ALT=\"+1%2Fz3+=++%2810-5i+%2B-3-4i%29%2F25\"   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=1%2Fz3+=%287-9i%29%2F25 ALIGN=MIDDLE  ALT=\"1%2Fz3+=%287-9i%29%2F25\"   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=z3=+25%2F%287-9i%29 ALIGN=MIDDLE  ALT=\"z3=+25%2F%287-9i%29\"   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=+z3=+%2825%2F%287-9i%29%29%2A%28%287%2B9i%29%2F%287%2B9i%29%29 ALIGN=MIDDLE  ALT=\"+z3=+%2825%2F%287-9i%29%29%2A%28%287%2B9i%29%2F%287%2B9i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z3+=+%2825%2A%287%2B9i%29%29%2F%2849-81i%5E2%29 ALIGN=MIDDLE  ALT=\"+z3+=+%2825%2A%287%2B9i%29%29%2F%2849-81i%5E2%29\"   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=+z3+=++%28175%2B225i%29%2F130 ALIGN=MIDDLE  ALT=\"+z3+=++%28175%2B225i%29%2F130\"   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=+z3=+%28175%2F130%29+%2B%28225%2F130%29+i ALIGN=MIDDLE  ALT=\"+z3=+%28175%2F130%29+%2B%28225%2F130%29+i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Simplify to get in standard form\r<BR>\n" );
document.write( "\n" );
document.write( "z3=1.346+1.731i\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );