`(1-i)^(4)`

Explanation

To solve the expression \((1 - i)^4\), we can follow these steps:

### Step 1: Expand \((1 - i)^4\) using the Binomial Theorem
The Binomial Theorem states that:
\[ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \]
In our case, \(a = 1\), \(b = -i\), and \(n = 4\).

Using the Binomial Theorem:
\[ (1 - i)^4 = \sum_{k=0}^{4} \binom{4}{k} (1)^{4-k} (-i)^k \]

### Step 2: Calculate each term of the expansion
Now we calculate each term for \(k = 0\) to \(k = 4\):
- For \(k = 0\):
\[ \binom{4}{0} (1)^{4} (-i)^{0} = 1 \]
- For \(k = 1\):
\[ \binom{4}{1} (1)^{3} (-i)^{1} = 4(-i) = -4i \]
- For \(k = 2\):
\[ \binom{4}{2} (1)^{2} (-i)^{2} = 6(-1) = -6 \]
- For \(k = 3\):
\[ \binom{4}{3} (1)^{1} (-i)^{3} = 4(-i^3) = 4i \]
(since \(i^3 = -i\))
- For \(k = 4\):
\[ \binom{4}{4} (1)^{0} (-i)^{4} = 1(1) = 1 \]
(since \(i^4 = 1\))

### Step 3: Combine all the terms
Now we combine all the terms:
\[ (1 - i)^4 = 1 - 4i - 6 + 4i + 1 \]

### Step 4: Simplify the expression
Combine like terms:
\[ (1 - 6 + 1) + (-4i + 4i) = -4 + 0i = -4 \]

### Final Answer
Thus, the value of \((1 - i)^4\) is:
\[ \boxed{-4} \]