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 #107940 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=107940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2F%282%2B5i%29 ALIGN=MIDDLE  ALT=\"%284%29%2F%282%2B5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%29%2F%282%2B5i%29%29%28%282-5i%29%2F%282-5i%29%29 ALIGN=MIDDLE  ALT=\"%28%284%29%2F%282%2B5i%29%29%28%282-5i%29%2F%282-5i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both numerator and denominator by the complex conjugate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B5i ALIGN=MIDDLE  ALT=\"2%2B5i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%29%282-5i%29%29%2F%28%282%2B5i%29%282-5i%29%29 ALIGN=MIDDLE  ALT=\"%28%284%29%282-5i%29%29%2F%28%282%2B5i%29%282-5i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%29%282-5i%29%29%2F%2829%29 ALIGN=MIDDLE  ALT=\"%28%284%29%282-5i%29%29%2F%2829%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil the denominator to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B5i%29%282-5i%29=4-10i%2B10i-25i%5E2=4-25%28-1%29=29 ALIGN=MIDDLE  ALT=\"%282%2B5i%29%282-5i%29=4-10i%2B10i-25i%5E2=4-25%28-1%29=29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288-20i%29%2F%2829%29 ALIGN=MIDDLE  ALT=\"%288-20i%29%2F%2829%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2F%282%2B5i%29=%288-20i%29%2F%2829%29 ALIGN=MIDDLE  ALT=\"%284%29%2F%282%2B5i%29=%288-20i%29%2F%2829%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E%28-35%29 ALIGN=MIDDLE  ALT=\"i%5E%28-35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fi%5E%2835%29 ALIGN=MIDDLE  ALT=\"1%2Fi%5E%2835%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the fraction to make the exponent positive.\r<BR>\n" );
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document.write( "Now let's find evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E%2835%29 ALIGN=MIDDLE  ALT=\"i%5E%2835%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "First take the exponent 35 and divide by 4.<BR>\n" );
document.write( "When it leaves a remainder of 0, the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "When it leaves a remainder of 1, the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29=i ALIGN=MIDDLE  ALT=\"sqrt%28-1%29=i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "When it leaves a remainder of 2, the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "When it leaves a remainder of 3, the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28-1%29=-i ALIGN=MIDDLE  ALT=\"-sqrt%28-1%29=-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2F4 ALIGN=MIDDLE  ALT=\"35%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > leaves a remainder of 3, this means the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i ALIGN=MIDDLE  ALT=\"-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E35=-i ALIGN=MIDDLE  ALT=\"i%5E35=-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fi%5E%2835%29=1%2F%28-i%29 ALIGN=MIDDLE  ALT=\"1%2Fi%5E%2835%29=1%2F%28-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28-i%29 ALIGN=MIDDLE  ALT=\"1%2F%28-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28-i%29%29%28i%2Fi%29 ALIGN=MIDDLE  ALT=\"%281%2F%28-i%29%29%28i%2Fi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both numerator and denominator by \"i\" \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Ai%29%2F%28%28-i%29%28i%29%29 ALIGN=MIDDLE  ALT=\"%281%2Ai%29%2F%28%28-i%29%28i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Ai%29%2F%28-i%5E2%29 ALIGN=MIDDLE  ALT=\"%281%2Ai%29%2F%28-i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Ai%29%2F%28-%28-1%29%29 ALIGN=MIDDLE  ALT=\"%281%2Ai%29%2F%28-%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28i%29%2F%281%29 ALIGN=MIDDLE  ALT=\"%28i%29%2F%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E%28-35%29=i ALIGN=MIDDLE  ALT=\"i%5E%28-35%29=i\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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