document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981120>Question 981120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please could someone help with this question. I can't get the last part.\r<BR>\n" );
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document.write( "Find real numbers a and b with a>0 such that:<BR>\n" );
document.write( "(a+ib)^2 = 1-1.875i\r<BR>\n" );
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document.write( "So far I have got this far.\r<BR>\n" );
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document.write( "a^2-b^2 +2abi = 1-1.875i<BR>\n" );
document.write( "Real: a^2-b^2=1   (1)<BR>\n" );
document.write( "Imaginary: 2ab = -1.875  (2)<BR>\n" );
document.write( "Divide imaginary part (2) becomes: a =-0.9375/b (3)<BR>\n" );
document.write( "I got 0.9375 =15/16\r<BR>\n" );
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document.write( "Sub in (1) gives:\r<BR>\n" );
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document.write( "(15/16)^2-b^4=b^2<BR>\n" );
document.write( "b^4+b^2-225/256=0<BR>\n" );
document.write( "From here I can not seem to factorize. Also I tried to use the quadratic formula but that didn't seem to work either.\r<BR>\n" );
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document.write( "Thank you in advance.<BR>\n" );
document.write( "The answer given in the textbook is: a=5/4 and b=-3/4\r<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 #602142 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=602142\">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=%28a%2Bbi%29%5E2=1-1.875i ALIGN=MIDDLE  ALT=\"%28a%2Bbi%29%5E2=1-1.875i\"   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=a%5E2%2B2abi%2Bb%5E2%2Ai%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B2abi%2Bb%5E2%2Ai%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=a%5E2%2Bb%5E2%2Ai%5E2%2B2abi ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2%2Ai%5E2%2B2abi\"   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=a%5E2%2Bb%5E2%28-1%29%2B2abi ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2%28-1%29%2B2abi\"   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=a%5E2-b%5E2%2B2abi=1-1.875i ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2%2B2abi=1-1.875i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Corresponding positions of the terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%5E2-b%5E2=1%2C2ab=-1.875%29 ALIGN=MIDDLE  ALT=\"system%28a%5E2-b%5E2=1%2C2ab=-1.875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the second equation and substitute for b in the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-%281.875%29%5E2%2F%284a%5E2%29=1 ALIGN=MIDDLE  ALT=\"a%5E2-%281.875%29%5E2%2F%284a%5E2%29=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=4a%5E4-4a%5E2-%281.875%29%5E2=0 ALIGN=MIDDLE  ALT=\"4a%5E4-4a%5E2-%281.875%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Things from this quadratic-form equation in \"a\" are not very neat.<BR>\n" );
document.write( "Some simplification after using formula for the general solution for quadratic equation gives  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28a%5E2=%281%2B-+sqrt%281%2B1.875%5E2%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28a%5E2=%281%2B-+sqrt%281%2B1.875%5E2%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, not yet a to first power, so not done yet..., but at least you are finding a real number for a.\r<BR>\n" );
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document.write( "Further computing for a^2 finally showed  (with handheld calculator help),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=1.5625 ALIGN=MIDDLE  ALT=\"a%5E2=1.5625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and since you're interested in positive values, find <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28a=1.25%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28a=1.25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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