document.write( "Question 802335: find the value of the following complex number: I^5 \n" ); document.write( "

Algebra.Com's Answer #483843 by DrBeeee(684) $\"\"$ $\"About$

You can put this solution on YOUR website!
What is $\"i%5E5\"$ ?
\n" ); document.write( "Let
\n" ); document.write( "(1) $\"i+=+sqrt%28-1%29\"$
\n" ); document.write( "Then
\n" ); document.write( "(2) $\"i%5E5+=+%28-1%29%5E%285%2F2%29\"$ or
\n" ); document.write( "(3) $\"i%5E5+=+sqrt%28%28-1%29%5E%285%29%29\"$ or
\n" ); document.write( "(4) $\"i%5E5+=+sqrt%28-1%29\"$ or
\n" ); document.write( "(5) $\"i%5E5+=+i\"$
\n" ); document.write( "Another way to show this is to use the polar form of i as
\n" ); document.write( "(6) i = 1 @ 90 deg
\n" ); document.write( "Then
\n" ); document.write( "(7) $\"i%5E5+=+1%5E5\"$ @ 5*90 deg or
\n" ); document.write( "(8) $\"i%5E5+=+1\"$ @ 450 deg or
\n" ); document.write( "(9) $\"i%5E5+=+1\"$ @ 90 deg or
\n" ); document.write( "(10) $\"i%5E5+=+i\"$ \n" ); document.write( "

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