For a positive integer n, what is the value of `i^(4n+1)` ?

Options

A. 1
B. `-1`
C. It is parallel to the y-axis
D. `-i`

Explanation

To solve the problem of finding the value of \( i^{4n+1} \) for a positive integer \( n \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression \( i^{4n+1} \). We can separate the exponent into two parts:
\[ i^{4n+1} = i^{4n} \cdot i^1 \]

### Step 2: Simplify \( i^{4n} \)
Next, we know that \( i^4 = 1 \). Therefore, we can express \( i^{4n} \) as:
\[ i^{4n} = (i^4)^n = 1^n = 1 \]

### Step 3: Combine the results
Now we can substitute back into our expression:
\[ i^{4n+1} = i^{4n} \cdot i^1 = 1 \cdot i = i \]

### Conclusion
Thus, the value of \( i^{4n+1} \) is:
\[ \boxed{i} \]