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 #843312 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=843312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B3%5D+=+35%2F26%2Bexpr%2845%2F26%29i ALIGN=MIDDLE  ALT=\"z%5B3%5D+=+35%2F26%2Bexpr%2845%2F26%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Work Shown\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28z%5B3%5D%29+=+1%2F%28z%5B1%5D%29%2B1%2F%28z%5B2%5D%29 ALIGN=MIDDLE  ALT=\"1%2F%28z%5B3%5D%29+=+1%2F%28z%5B1%5D%29%2B1%2F%28z%5B2%5D%29\"   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=1%2F%28z%5B3%5D%29+=+%28z%5B2%5D%29%2F%28z%5B1%5Dz%5B2%5D%29%2B%28z%5B1%5D%29%2F%28z%5B1%5Dz%5B2%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Get every fraction on the right hand side in terms of the LCD\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28z%5B3%5D%29+=+%28z%5B2%5D%2Bz%5B1%5D%29%2F%28z%5B1%5Dz%5B2%5D%29 ALIGN=MIDDLE  ALT=\"1%2F%28z%5B3%5D%29+=+%28z%5B2%5D%2Bz%5B1%5D%29%2F%28z%5B1%5Dz%5B2%5D%29\"   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=z%5B3%5D+=+%28z%5B1%5Dz%5B2%5D%29%2F%28z%5B2%5D%2Bz%5B1%5D%29 ALIGN=MIDDLE  ALT=\"z%5B3%5D+=+%28z%5B1%5Dz%5B2%5D%29%2F%28z%5B2%5D%2Bz%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply reciprocal to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B3%5D+=+%28%282%2Bi%29%28-3%2B4i%29%29%2F%28-3%2B4i%2B2%2Bi%29 ALIGN=MIDDLE  ALT=\"z%5B3%5D+=+%28%282%2Bi%29%28-3%2B4i%29%29%2F%28-3%2B4i%2B2%2Bi%29\"   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=z%5B3%5D+=+%28-10%2B5i%29%2F%28-1%2B5i%29 ALIGN=MIDDLE  ALT=\"z%5B3%5D+=+%28-10%2B5i%29%2F%28-1%2B5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  See scratch work section shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B3%5D+=+%28%28-10%2B5i%29%28-1-5i%29%29%2F%28%28-1%2B5i%29%28-1-5i%29%29 ALIGN=MIDDLE  ALT=\"z%5B3%5D+=+%28%28-10%2B5i%29%28-1-5i%29%29%2F%28%28-1%2B5i%29%28-1-5i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply top and bottom by conjugate of the denominator so the denominator becomes a real number.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B3%5D+=+%2835%2B45i%29%2F%2826%29 ALIGN=MIDDLE  ALT=\"z%5B3%5D+=+%2835%2B45i%29%2F%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Follow similar steps as the scratch work section shown below. Note: (a+bi)(a-bi) = a^2+b^2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B3%5D+=+35%2F26%2Bexpr%2845%2F26%29i ALIGN=MIDDLE  ALT=\"z%5B3%5D+=+35%2F26%2Bexpr%2845%2F26%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Complex number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B3%5D ALIGN=MIDDLE  ALT=\"z%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is of the form a+bi where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+35%2F26 ALIGN=MIDDLE  ALT=\"a+=+35%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+45%2F26 ALIGN=MIDDLE  ALT=\"b+=+45%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Scratch Work\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Bi%29%28-3%2B4i%29+=+-6%2B8i-3i%2B4i%5E2 ALIGN=MIDDLE  ALT=\"%282%2Bi%29%28-3%2B4i%29+=+-6%2B8i-3i%2B4i%5E2\"   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=%282%2Bi%29%28-3%2B4i%29+=+-6%2B8i-3i-4 ALIGN=MIDDLE  ALT=\"%282%2Bi%29%28-3%2B4i%29+=+-6%2B8i-3i-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Another approach for this scratch work section is to use the FOIL rule or the box method.<BR>\n" );
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