document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762782>Question 762782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to solve i^15 step by step </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464195 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=464195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i^15\r<BR>\n" );
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document.write( "i^(12+3)\r<BR>\n" );
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document.write( "i^(12)*i^3\r<BR>\n" );
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document.write( "(i^(3*4))*i^3\r<BR>\n" );
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document.write( "(i^3)^4*i^3\r<BR>\n" );
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document.write( "(-i)^4*(-i)\r<BR>\n" );
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document.write( "(-1)^4*(i)^4*(-i)\r<BR>\n" );
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document.write( "(-1)^4*(i^2)^2*(-i)\r<BR>\n" );
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document.write( "(-1)^4*(-1)^2*(-i)\r<BR>\n" );
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document.write( "(-1)^4*1*(-i)\r<BR>\n" );
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document.write( "(-1)^4*(-i)\r<BR>\n" );
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document.write( "1*(-i)\r<BR>\n" );
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document.write( "-i\r<BR>\n" );
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document.write( "So i^15 = -i\r<BR>\n" );
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document.write( "Shortcut: divide 15 by 4 to get 3 remainder 3. The remainder of 3 means that i^(15) = i^3. Since i^3 = -i, this means i^15 = -i </SPAN>\n" );
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