Find the modulus of `(1+i)/(1-i)-(1-i)/(1+i)`.

Explanation

To find the modulus of the expression \((1+i)/(1-i)-(1-i)/(1+i)\), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{1+i}{1-i} - \frac{1-i}{1+i} \]

### Step 2: Find a common denominator
The common denominator for the two fractions is \((1-i)(1+i)\). We rewrite the expression:
\[ \frac{(1+i)(1+i) - (1-i)(1-i)}{(1-i)(1+i)} \]

### Step 3: Simplify the numerator
Now, we simplify the numerator:
\[ (1+i)(1+i) = 1 + 2i + i^2 = 1 + 2i - 1 = 2i \]
\[ (1-i)(1-i) = 1 - 2i + i^2 = 1 - 2i - 1 = -2i \]
So the numerator becomes:
\[ 2i - (-2i) = 2i + 2i = 4i \]

### Step 4: Simplify the denominator
Now, we simplify the denominator:
\[ (1-i)(1+i) = 1^2 - i^2 = 1 - (-1) = 2 \]

### Step 5: Combine the results
Now we can rewrite the expression:
\[ \frac{4i}{2} = 2i \]

### Step 6: Find the modulus
To find the modulus of \(2i\):
\[ |2i| = \sqrt{(0)^2 + (2)^2} = \sqrt{4} = 2 \]

### Final Answer
Thus, the modulus of the given expression is:
\[ \boxed{2} \]