Simplify:
`(1)/(i) + (1)/(i^(2)) + (1)/(i^(3)) + (1)/(i^(4))`

Answer

To simplify the expression \( \frac{1}{i} + \frac{1}{i^2} + \frac{1}{i^3} + \frac{1}{i^4} \), we will follow these steps:

### Step 1: Evaluate each term
First, we need to evaluate each term in the expression using the powers of \( i \) (where \( i = \sqrt{-1} \)):
- \( i^1 = i \)
- \( i^2 = -1 \)
- \( i^3 = i^2 \cdot i = -1 \cdot i = -i \)
- \( i^4 = (i^2)^2 = (-1)^2 = 1 \)

### Step 2: Substitute the values into the expression
Now we can substitute these values back into the expression:
\[ \frac{1}{i} + \frac{1}{-1} + \frac{1}{-i} + \frac{1}{1} \]
This simplifies to:
\[ \frac{1}{i} - 1 - \frac{1}{i} + 1 \]

### Step 3: Combine like terms
Next, we can combine like terms:
- The \( -1 \) and \( +1 \) cancel each other out:
\[ \frac{1}{i} - \frac{1}{i} = 0 \]

### Step 4: Final result
Thus, the final result of the expression is:
\[ 0 \]

### Summary of the solution
The simplified expression is \( 0 \).