document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987630>Question 987630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . From the set {6i, -4/5, &#8730;5, &#8730;-16, 2/7, 12, -5, &#8730;9, 1/3}<BR>\n" );
document.write( "a)	List the set of Natural numbers = <BR>\n" );
document.write( "b)	List the set of Rational numbers =<BR>\n" );
document.write( "c)	List the set of Irrational numbers =<BR>\n" );
document.write( "d)	List the set of Imaginary numbers (neither Rational or Irrational Numbers) = <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 #608389 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=608389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "12 is the only natural number.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{4}{5},\ \frac{2}{7},\ 12,\ \sqrt{9},\ -5,\ \frac{1}{3}\"> are rational\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{5}\"> is irrational.\r<BR>\n" );
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document.write( "Saying \"the set of Imaginary numbers\" is a poor way to describe things.  In fact there is only one Imaginary number and that is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\"> which is defined as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i^2\ =\ -1\">.\r<BR>\n" );
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document.write( "Everything else someone might have told you is a member of the set of Imaginary numbers is simply <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\"> with some  real number coefficient.  The actual set is the set of Complex numbers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \mathbb{C}\ =\ \left\{a\ +\ bi\ |\ a,b\ \in\ \mathbb{R},\ i^2\ =\ -1\right\}\">\r<BR>\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 6i\"> is a complex number of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\ +\ 6i\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{-16}\"> is a complex number of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\ +\ 4i\">\r<BR>\n" );
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document.write( "Note that the set of Real numbers is a subset of the Complex numbers, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \mathbb{R}\ =\ \left\{a\ +\ bi\ \in\ \mathbb{C}\ |\ b\ =\ 0\right\}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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