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 \(1 - i\), the second root will be its complex conjugate, which is \(1 + i\).

### Step 2: Calculate the sum of the roots
The sum of the roots \(S\) can be calculated as:
\[ S = (1 - i) + (1 + i) = 1 - i + 1 + i = 2 \]

### Step 3: Calculate the product of the roots
The product of the roots \(P\) can be calculated as:
\[ P = (1 - i)(1 + i) \]
Using the identity \(a^2 - b^2 = (a - b)(a + b)\), we have:
\[ P = 1^2 - i^2 = 1 - (-1) = 1 + 1 = 2 \]

### Step 4: Form the quadratic equation
The general form of a quadratic equation with roots \(r_1\) and \(r_2\) is given by:
\[ x^2 - (S)x + P = 0 \]
Substituting the values of \(S\) and \(P\):
\[ x^2 - (2)x + 2 = 0 \]

### Final Result
Thus, the quadratic equation is:
\[ x^2 - 2x + 2 = 0 \]

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