Find the quadratic equation whose one root is `(1-i)`.

Explanation

To find the quadratic equation whose one root is \(1 - i\), we can follow these steps:

### Step 1: Identify the roots
Given that one root is \(1 - i\), we can find the second root, which is the complex conjugate of the first root. The complex conjugate of \(1 - i\) is \(1 + i\).

### Step 2: Calculate the sum of the roots
The sum of the roots \(r_1\) and \(r_2\) can be calculated as follows:
\[ r_1 + r_2 = (1 - i) + (1 + i) \]
When we simplify this:
\[ = 1 - i + 1 + i = 2 \]

### Step 3: Calculate the product of the roots
The product of the roots can be calculated using the formula for the product of two conjugates:
\[ r_1 \cdot r_2 = (1 - i)(1 + i) \]
Using the difference of squares formula \(a^2 - b^2\), where \(a = 1\) and \(b = i\):
\[ = 1^2 - i^2 = 1 - (-1) = 1 + 1 = 2 \]

### Step 4: Form the quadratic equation
The general form of a quadratic equation is given by:
\[ x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0 \]
Substituting the values we found:
\[ x^2 - (2)x + (2) = 0 \]
This simplifies to:
\[ x^2 - 2x + 2 = 0 \]

### Final Answer
The quadratic equation whose one root is \(1 - i\) is:
\[ \boxed{x^2 - 2x + 2 = 0} \]