document.write( "Question 134532: How would you solve the problem i^7+i^2+i^12+i^9 over (1-i)^2? \n" ); document.write( "

Algebra.Com's Answer #98416 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28i%5E7%2Bi%5E2%2Bi%5E12%2Bi%5E9%29+%2F+%281-i%29%5E2\"$
\n" ); document.write( "Note that
\n" ); document.write( " $\"i%5E1+=+i\"$
\n" ); document.write( " $\"i%5E2+=+-1\"$
\n" ); document.write( " $\"i%5E3+=+-1%2Ai\"$
\n" ); document.write( " $\"i%5E4+=+-1%2A-1\"$
\n" ); document.write( " $\"i%5E5+=+-1%2A-1%2Ai\"$
\n" ); document.write( " $\"i%5E6+=+-1%2A-1%2A-1\"$
\n" ); document.write( " $\"i%5E7+=+-1%2A-1%2A-1%2Ai\"$
\n" ); document.write( " $\"i%5E8+=+-1%2A-1%2A-1%2A-1\"$
\n" ); document.write( "So, the sequence is
\n" ); document.write( "i, -1, -i, 1, i, -1, -i, 1
\n" ); document.write( "If the exponent is 1,5,9,13. . . every other odd #, then
\n" ); document.write( " $\"i%5En+=+i\"$
\n" ); document.write( "If the exponent is 3,7,11,15 . . .every other odd #, then
\n" ); document.write( " $\"i%5En+=+-i\"$
\n" ); document.write( "If the exponent is 2,6,10,14 . . .every other even #, then
\n" ); document.write( " $\"i%5En+=+-1\"$
\n" ); document.write( "If the exponent is 4,8,12,16 . . .every other even #, then
\n" ); document.write( " $\"i%5En+=+1\"$
\n" ); document.write( " $\"%28i%5E7+%2B+i%5E2+%2B+i%5E12+%2B+i%5E9%29+%2F+%281-i%29%5E2\"$
\n" ); document.write( " $\"%28-i+%2B+%28-1%29+%2B+1+%2B+i%29+%2F+%281+-2i+%2B+%28-1%29%29\"$
\n" ); document.write( " $\"0+%2F+%28-2i%29\"$
\n" ); document.write( "Unless I goofed, the answer is $\"0\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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