How do you simplify `i^13` ?
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Lix Lemjay
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calendarEducator since 2012
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To simplify `i^n` , divide the exponent by 4. Then, consider only the remainder of the quotient.
>> If remainder is 0 ,then `i^n=1` .
>> If reminder is 1, then `i^n=i` .
>> If remainder is 2, then `i^n=-1` .
>> If remainder is 3, then `i^n=-i` .
Applying this, the remainder of `i^13` is:
13 `-:` 4 = 3 Remainder 1
Hence, `i^13=i` .
Another way is to breakdown `i^13` to factors of `i^4` .
`i^13=i^4*i^4*i^4*i=(i^4)^3*i`
Since `i^4=1` , then
`=(1)^3*i=1*i=i`
Thus, either method results to `i^13=i` .
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