document.write( "Question 14062: What is i83= Thank you. I need before 12:00 and could explain why the pattern of imaginary numbers repeat themselves? It would really help me on my test tommorrow!!!!!!!!!!!!1 \n" ); document.write( "

Algebra.Com's Answer #7073 by bam878s(77) $\"\"$ $\"About$

You can put this solution on YOUR website!
note $\"i%5E83\"$ = $\"i%5E80%2Ai%5E3\"$ .
\n" ); document.write( "we have $\"i%5E80+%2A+%28-i%29\"$ since i^3 = -i.
\n" ); document.write( "and $\"i%5E80\"$ = $\"%28i%5E2%29%5E40\"$ .
\n" ); document.write( "we know $\"i%5E2\"$ = -1.
\n" ); document.write( "so what we have $\"%28-1%29%5E40+%2A+%28-i%29\"$ .
\n" ); document.write( "we know $\"%28-1%29%5Eevenpower\"$ =1
\n" ); document.write( "and $\"%28-1%29%5Eoddpower\"$ = -1.
\n" ); document.write( "since 40 is even $\"%28-1%29%5E40\"$ = 1
\n" ); document.write( "so we have $\"1%2A%28-i%29\"$ = -i.
\n" ); document.write( "Hope this helps you again. \n" ); document.write( "

\n" );