To calculate: i^{1000} + i^{1002}

djeljenike

djeljenike

Answered question

2021-08-10

To calculate: The simplified expression for the expression i1000+i1002

Answer & Explanation

krolaniaN

krolaniaN

Skilled2021-08-11Added 86 answers

Formula used:
By the definition of i=1, it follows that:
i2=1
i3=i
i4=1
To simplify higher powers of i, decompose the expression into multiples of i4 and write the remaining factors as i,i2 or i3.
Calculation:
Consider the provided expression:
i1000+i1002
Now, to simplify higher powers of i, decompose the expression into multiples of i4(i4=1) and write the remaining factors as i,i2 or i3.
Thus, for the provoded expression:
i1000+i1002=i4(250)+i4(250)i2
=1250+1250i2
Now, as i2=1, thus:
i1000+i1002=1250+1250i2
=1+(1)
=0
Thus, the simplified expression for the expression i1000+i1002 is 0.

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