The amplitude of `1/i` is equal to-

Options

A. `0`
B. `pi/2`
C. `-pi/2`
D. `pi`

Explanation

To find the amplitude (or argument) of the complex number \( \frac{1}{i} \), we will follow these steps:

### Step 1: Simplify the complex number
We start with the complex number \( z = \frac{1}{i} \). To simplify this, we can multiply the numerator and the denominator by \( i \):

\[ z = \frac{1}{i} \cdot \frac{i}{i} = \frac{i}{i^2} \]

### Step 2: Use the property of \( i^2 \)
We know that \( i^2 = -1 \). Therefore, we can substitute this into our expression:

\[ z = \frac{i}{-1} = -i \]

### Step 3: Identify the real and imaginary parts
Now, we have \( z = -i \). In standard form \( a + bi \), we can identify \( a = 0 \) and \( b = -1 \).

### Step 4: Determine the quadrant
Next, we need to locate the complex number in the Argand plane. Since \( a = 0 \) and \( b = -1 \), the point lies on the negative imaginary axis, specifically at the coordinates \( (0, -1) \). This point is located in the fourth quadrant.

### Step 5: Find the argument
The argument (or amplitude) of a complex number \( z = a + bi \) can be found using the formula:

\[ \theta = \tan^{-1}\left(\frac{b}{a}\right) \]

In our case, since \( a = 0 \) and \( b = -1 \):

\[ \frac{b}{a} = \frac{-1}{0} \]

This is undefined, which indicates that the angle is either \( \frac{\pi}{2} \) or \( -\frac{\pi}{2} \). Since our point is in the fourth quadrant, the argument is:

\[ \theta = -\frac{\pi}{2} \]

### Step 6: Conclusion
Thus, the amplitude of \( \frac{1}{i} \) is:

\[ \boxed{-\frac{\pi}{2}} \]

---