document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=396764>Question 396764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, how do I figure out this complex numbers problem? Any help is greatly appreciated!\r<BR>\n" );
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document.write( "The point (-4+bi)has been plotted on the complex plane and r=8. If 0°&#8804;&#952;&#8804;180° find the value of b. Leave answer as a radical.\r<BR>\n" );
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document.write( "Thank you.<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 #281390 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=281390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The \"a\" and \"b\" in standard form and the \"r\" in polar form are related by the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subsituting the value we have for \"a\" and \"r\" we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%5E2+%2B+b%5E2+=+%288%29%5E2 ALIGN=MIDDLE  ALT=\"%28-4%29%5E2+%2B+b%5E2+=+%288%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+%2B+b%5E2+=+64 ALIGN=MIDDLE  ALT=\"16+%2B+b%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting 16 we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+48 ALIGN=MIDDLE  ALT=\"b%5E2+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we find the square root of each side. Since the theta is between 0 and 180, we want \"b\" to be positive. (A negative \"b\" would put theta between 180 and 360.) So we will only use the positive square root:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%2848%29 ALIGN=MIDDLE  ALT=\"b+=+sqrt%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All that is left is simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%2816%2A3%29 ALIGN=MIDDLE  ALT=\"b+=+sqrt%2816%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%2816%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"b+=+sqrt%2816%29%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"b+=+4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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