document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=719085>Question 719085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three impedances are connected in parallel,<BR>\n" );
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document.write( "Z1 = 2+j2<BR>\n" );
document.write( "Z2 = 1+j5 and<BR>\n" );
document.write( "Z3 = j6<BR>\n" );
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document.write( "Find the equivalent admittance Y<BR>\n" );
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document.write( "Where:<BR>\n" );
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document.write( "Y= 1/Z1 + 1/Z2 + 1/Z3<BR>\n" );
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document.write( "Express in both rectangular and polar forms.<BR>\n" );
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document.write( "I am currently struggling on Z3= j6,but clarification on the rest would be a great help. \r<BR>\n" );
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document.write( "Thanks<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #441191 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=441191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=1%2F%282%2Bj2%29%2B1%2F%281%2Bj5%29%2B1%2F%28j6%29 ALIGN=MIDDLE  ALT=\"Y=1%2F%282%2Bj2%29%2B1%2F%281%2Bj5%29%2B1%2F%28j6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Each term can be transformed by multiplying numerator and denominator times the conjugate of the denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=1%2A%282-j2%29%2F%282%2Bj2%29%2F%282-j2%29%2B1%2A%281-j5%29%2F%281%2Bj5%29%2F%281-j5%29%2B1%2A%28-j6%29%2F%28j6%29%2F%28-j6%29=%282-j2%29%2F%284-j%5E2%2A4%29%2B%281-j5%29%2F%281-j%5E2%2A25%29%2B%28-j6%29%2F%28-j%5E2%2A36%29=%282-j2%29%2F%284%2B4%29%2B%281-j5%29%2F%281%2B25%29-j6%2F36=%282-j2%29%2F8%2B%281-j5%29%2F26-j6%2F36 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=936=26%2A36=13%2A2%2A4%2A9=13%2A8%2A9=8%2A%289%2A13%29=8%2A117 ALIGN=MIDDLE  ALT=\"936=26%2A36=13%2A2%2A4%2A9=13%2A8%2A9=8%2A%289%2A13%29=8%2A117\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a good common denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%28117%282-j2%29%2B36%281-j5%29%2B26%28-j6%29%29%2F936=%28234-j234%2B36-j180-156%29%2F936=%28270-j570%29%2F936 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That can be expressed as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=270%2F936-%28570%2F936%29j=15%2F52-%2895%2F156%29j ALIGN=MIDDLE  ALT=\"Y=270%2F936-%28570%2F936%29j=15%2F52-%2895%2F156%29j\"   DISABLED_style= \"max-width:90%; height:auto;\" >= approximately<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.288-0.609j ALIGN=MIDDLE  ALT=\"0.288-0.609j\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Unless your problem is just a math exercise, you would use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.288-0.609j ALIGN=MIDDLE  ALT=\"0.288-0.609j\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which provides enough decimal places for practical purposes.<BR>\n" );
document.write( "For the polar form we know that the absolute value would be<BR>\n" );
document.write( "r=approximately<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%280.288%5E2%2B0.609%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%280.288%5E2%2B0.609%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= approximately<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.674 ALIGN=MIDDLE  ALT=\"0.674\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If this was just a math exercise, and an exact value was required,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%28%28270%2F936%29%5E2%2B%28570%2F936%29%5E2%29=sqrt%28397800%2F936%5E2%29=30sqrt%28442%29%2F936 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be such that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=-570%2F270=-19%2F9 ALIGN=MIDDLE  ALT=\"tan%28theta%29=-570%2F270=-19%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >= approximately<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.111 ALIGN=MIDDLE  ALT=\"-2.111\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That corresponds to approximately<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=-1.128 ALIGN=MIDDLE  ALT=\"theta=-1.128\"   DISABLED_style= \"max-width:90%; height:auto;\" > in radians or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=-64.7%5Eo ALIGN=MIDDLE  ALT=\"theta=-64.7%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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