document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4786>Question 4786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello...\r<BR>\n" );
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document.write( "I am having some trouble with a proof.  I am to use:\r<BR>\n" );
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document.write( "(a + bi)(a - bi)\r<BR>\n" );
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document.write( "The problem asks:\r<BR>\n" );
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document.write( "Show that for a + bi not equal to 0 this product is a positive real number.\r<BR>\n" );
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document.write( "Thanks for your help.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2284 by </B><A HREF=/tutors/aboutme.mpl?userid=ichudov><B>ichudov(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ichudov><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=ichudov><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2284\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The question is wrong. there are values of a and b that make the above product a non positive (zero) number. However, the product is always non-negative (non-negative numbers include positive numbers and zero).\r<BR>\n" );
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document.write( "Proving it it is very easy. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bbi%29%2A%28a-bi%29+=+a%5E2-%28bi%29%5E2+=+a%5E2+-+b%5E2i%5E2+=+a%5E2-b%5E2%2A%28-1%29+=+a%5E2%2Bb%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "sub of two squares <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is always non-negative. </SPAN>\n" );
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