`i`

Explanation

To convert the complex number \( i \) into polar form, we can follow these steps:

### Step 1: Identify the Complex Number
The complex number given is \( i \), which can be expressed as:
\[ 0 + i \quad \text{(where the real part is 0 and the imaginary part is 1)} \]

### Step 2: Write in the Form \( r(\cos \theta + i \sin \theta) \)
The polar form of a complex number is given by:
\[ r(\cos \theta + i \sin \theta) \]
where \( r \) is the modulus and \( \theta \) is the argument of the complex number.

### Step 3: Calculate the Modulus \( r \)
The modulus \( r \) is calculated using the formula:
\[ r = \sqrt{a^2 + b^2} \]
where \( a \) is the real part and \( b \) is the imaginary part. For our complex number:
\[ r = \sqrt{0^2 + 1^2} = \sqrt{1} = 1 \]

### Step 4: Calculate the Argument \( \theta \)
The argument \( \theta \) can be found using:
\[ \cos \theta = \frac{a}{r} \quad \text{and} \quad \sin \theta = \frac{b}{r} \]
Substituting the values:
\[ \cos \theta = \frac{0}{1} = 0 \quad \text{and} \quad \sin \theta = \frac{1}{1} = 1 \]

### Step 5: Determine \( \theta \)
The angle \( \theta \) where \( \cos \theta = 0 \) and \( \sin \theta = 1 \) is:
\[ \theta = \frac{\pi}{2} \quad \text{(in radians)} \]

### Step 6: Write the Polar Form
Now, substituting \( r \) and \( \theta \) into the polar form:
\[ i = 1(\cos \frac{\pi}{2} + i \sin \frac{\pi}{2}) \]

### Final Result
Thus, the polar form of the complex number \( i \) is:
\[ i = 1 \left( \cos \frac{\pi}{2} + i \sin \frac{\pi}{2} \right) \]

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