Find the modulus of the complex number:
`(1)/(2-3i)`.

Answer

To find the modulus of the complex number \( z = \frac{1}{2 - 3i} \), we will follow these steps:

### Step 1: Write the modulus property
We know that the modulus of a quotient of complex numbers can be expressed as:
\[ |z| = \left| \frac{1}{2 - 3i} \right| = \frac{|1|}{|2 - 3i|} \]

### Step 2: Calculate the modulus of the numerator
The modulus of the numerator \( |1| \) is:
\[ |1| = 1 \]

### Step 3: Calculate the modulus of the denominator
Next, we need to calculate the modulus of the denominator \( |2 - 3i| \). The modulus of a complex number \( a + bi \) is given by:
\[ |a + bi| = \sqrt{a^2 + b^2} \]
For our case, \( a = 2 \) and \( b = -3 \):
\[ |2 - 3i| = \sqrt{2^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13} \]

### Step 4: Substitute back into the modulus formula
Now we substitute back into our modulus formula:
\[ |z| = \frac{|1|}{|2 - 3i|} = \frac{1}{\sqrt{13}} \]

### Step 5: Final result
Thus, the modulus of the complex number \( \frac{1}{2 - 3i} \) is:
\[ |z| = \frac{1}{\sqrt{13}} \]