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Evaluate : (i) i^(23)" "(ii) i^(9...

Evaluate :
`(i) i^(23)" "(ii) i^(998)" "(iii)i^(-998)" "(iv) i^(-71)`
`(v) (sqrt(-1))^(91)" "(vi) (i^(37)xx i^(-61))" "(vii) i^(-1)`

Text Solution

AI Generated Solution

To evaluate the expressions involving the imaginary unit \( i \), we can use the fact that \( i^2 = -1 \) and the powers of \( i \) cycle every four terms: - \( i^1 = i \) - \( i^2 = -1 \) - \( i^3 = -i \) - \( i^4 = 1 \) From this, we can derive the following evaluations for each part of the question: ...
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