document.write( "Question 542668: Solve i^-4003 \n" ); document.write( "

Algebra.Com's Answer #354657 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
When plotting imaginary and real numbers, the
\n" ); document.write( "vertical axes are imaginary.
\n" ); document.write( "For a rotating vector of length 1, the sequence is:
\n" ); document.write( "i, -1, -i, 1
\n" ); document.write( "and this just keeps repeating as the vector rotates
\n" ); document.write( " $\"+i%5E%28-4003%29+\"$
\n" ); document.write( "This is a vector that rotates in the opposite direction
\n" ); document.write( "the sequence is:
\n" ); document.write( "-i, -1, i, 1
\n" ); document.write( "The vector goes around $\"+4003%2F4+\"$ times, because
\n" ); document.write( "every 4 steps brings it back to $\"+-i+\"$
\n" ); document.write( " $\"+4003%2F4+=+1000+\"$ with a remainder of $\"+3+\"$
\n" ); document.write( "1 step puts me at $\"-1\"$
\n" ); document.write( "2 steps puts me at $\"+i+\"$
\n" ); document.write( "3 steps puts me at $\"+1+\"$
\n" ); document.write( " $\"+i%5E%28-4003%29+=+1+\"$
\n" ); document.write( "Hope I got it. You might want
\n" ); document.write( "another opinion in case I messed up.\r
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