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Prove that: (i) 1+i^(10)+i^(100)-i^(10...

Prove that:
(i) `1+i^(10)+i^(100)-i^(1000)=0`
(ii) `i^(107)+i^(112)+i^(117)+i^(122)=0`
(iii) `(1+i^(14)+i^(18)+i^(22))` is real number.

Text Solution

Verified by Experts

The correct Answer is:
(i) `1+(1)^(2)xx(-1)+(1)^(25)-(1)^(250)`
(ii) 0
(iii) `-2`
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