document.write( "Question 133841: i^55 \n" ); document.write( "

Algebra.Com's Answer #97891 by solver91311(24713) $\"\"$ $\"About$

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$\"red%28i%5E0%29=1\"$ because anything to the zero power is 1
\n" ); document.write( " $\"red%28i%5E1%29=i\"$ because anything to the 1 power is itself
\n" ); document.write( " $\"red%28i%5E2%29=-1\"$ by definition of i
\n" ); document.write( " $\"red%28i%5E3%29=i%5E2%2Ai%5E1=-1%2Ai=-i\"$ because $\"a%5En%2Aa%5Em=a%5E%28n%2Bm%29\"$
\n" ); document.write( " $\"i%5E4=i%5E2%2Ai%5E2=-1%2A-1=1=red%28i%5E0%29\"$
\n" ); document.write( " $\"i%5E5=i%5E4%2Ai%5E1=1%2Ai=i=red%28i%5E1%29\"$
\n" ); document.write( " $\"i%5E6=i%5E4%2Ai%5E2=1%2A-1=-1=red%28i%5E2%29\"$ , and
\n" ); document.write( " $\"i%5E7=i%5E4%2Ai%5E3=1%2A%28-i%29=%28-i%29=red%28i%5E3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "And the pattern repeats forever.\r
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\n" ); document.write( "\n" ); document.write( "So, the process is to take the exponent on i, 55 in this case and perform integer division with a divisor of 4. Integer division is the first kind of division you learned in the 2nd or 3rd grade where you got a quotient and a remainder. Then raise i to the power of the remainder.\r
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\n" ); document.write( "\n" ); document.write( " $\"55%2F4=13r3\"$ , so $\"i%5E55=i%5E3=-i\"$ \n" ); document.write( "

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