document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469997>Question 469997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the expression and write the answer in a+bi form. \r<BR>\n" );
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document.write( "5/(3-4i) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322426 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=322426\">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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{5}{3\ -\ 4i}\">\r<BR>\n" );
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document.write( "Five principles required.\r<BR>\n" );
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document.write( "1.  Anything divided by itself is 1, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{a}{a}\ =\ 1\ \forall\ a\ \in\ \mathbb{C}\">\r<BR>\n" );
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document.write( "2.  1 is the multiplicative identity, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\ \cdot\ 1\ =\ a\ \forall\ a\ \in\ \mathbb{C}\">\r<BR>\n" );
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document.write( "3.  The product of a pair of conjugate binomials is the difference of 2 squares, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (a\ +\ b)(a\ -\ b)\ =\ a^2\ -\ b^2\">\r<BR>\n" );
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document.write( "4.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE i^2\ =\ -1\">\r<BR>\n" );
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document.write( "Combining 3 and 4, we can show that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (a\ +\ bi)(a\ -\ bi)\ =\ a^2\ +\ b^2\">\r<BR>\n" );
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document.write( "5.  Multiplication of a complex number by a real number is defined as: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  c(a\ +\ bi)\ =\ ac\ +\ bci\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{5}{3\ -\ 4i}\">\r<BR>\n" );
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document.write( "Apply principles 1 and 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{5}{3\ -\ 4i}\right)\left(\frac{3\ +\ 4i}{3\ +\ 4i}\right)\">\r<BR>\n" );
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document.write( "Apply principles 3, 4, and 5 and the definition of multiplication of fractions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{15\ +\ 20i}{25}\">\r<BR>\n" );
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document.write( "Simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3}{5}\ +\ \frac{4i}{5}\">\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<BR>\n" );
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