document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147558>Question 147558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm not quite sure how to simplify the expression 4 over 2+5i (4/2+5i) and I'm not quite sure what i to the -35th power means. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107942 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=107942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm not quite sure how to simplify the expression 4 over 2+5i (4/2+5i) and I'm not quite sure what i to the -35th power means.<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "4/(2+5i)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Multiply numerator and denominator by (2-5i) to get:<BR>\n" );
document.write( "[4(2-5i)]/[4+25]<BR>\n" );
document.write( "= (8-20i)/29<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "i^(-35)<BR>\n" );
document.write( "Applying the -1 exponent you get:<BR>\n" );
document.write( "(i^3)^35<BR>\n" );
document.write( "Applying the 35 exponent you get:<BR>\n" );
document.write( "= i^105\r<BR>\n" );
document.write( "\n" );
document.write( "= i^(104+1)\r<BR>\n" );
document.write( "\n" );
document.write( "= i^(104) * i^1\r<BR>\n" );
document.write( "\n" );
document.write( "= 1 * i^1\r<BR>\n" );
document.write( "\n" );
document.write( "= i<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );