Find the values of following expressions: `i^(49)+i^(68)+i^(89)+i^(110)` (ii) `i^(30)+i^(80)+i^(120)` (iii) `i^+i^2+i^3+i^4` (iv) `i^5+i^(10)+i^(15)` (v) `(i^(592)+i^(590)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(576)+i^(574))` (vi) `1+i^2+i^4+i^6+i^8+doti^(20)` (vii) `(1+i)^6+(1-i)^3`

Explanation

To solve the given expressions involving powers of the imaginary unit \( i \), we will use the fact that \( i^2 = -1 \) and the periodicity of powers of \( i \) which repeats every four terms:

- \( i^1 = i \)
- \( i^2 = -1 \)
- \( i^3 = -i \)
- \( i^4 = 1 \)
- \( i^5 = i \), and so on.

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