The value of `(i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(578)+i^(576)+i^(574))-1\ ` is a. `-1` b. `-2` c. `-3` d. `-4`

Explanation

To solve the expression \(\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1\), we will follow these steps:

### Step 1: Simplify the powers of \(i\)
The powers of \(i\) cycle every 4 terms:
- \(i^0 = 1\)
- \(i^1 = i\)
- \(i^2 = -1\)
- \(i^3 = -i\)
...