If z is a complex number, then the minimum value of `|z - 2.8| + |z - 1.42|` is ____________

Answer

To find the minimum value of the expression \( |z - 2.8| + |z - 1.42| \), we can use the properties of complex numbers and the triangle inequality.

### Step-by-Step Solution:

1. **Understanding the Expression**:
We are given the expression \( |z - 2.8| + |z - 1.42| \). Here, \( z \) is a complex number, and \( 2.8 \) and \( 1.42 \) are real numbers on the complex plane.

2. **Applying the Triangle Inequality**:
According to the triangle inequality, for any complex numbers \( a \) and \( b \):
\[ |a| + |b| \geq |a - b| \]
We can set \( a = z - 2.8 \) and \( b = z - 1.42 \).

3. **Rearranging the Terms**:
We need to express the inequality in terms of \( z \):
\[ |z - 2.8| + |z - 1.42| \geq |(z - 2.8) - (z - 1.42)| \]
Simplifying the right-hand side:
\[ |(z - 2.8) - (z - 1.42)| = |1.42 - 2.8| = |-1.38| = 1.38 \]

4. **Finding the Minimum Value**:
Therefore, we conclude that:
\[ |z - 2.8| + |z - 1.42| \geq 1.38 \]
The minimum value of the expression \( |z - 2.8| + |z - 1.42| \) is thus \( 1.38 \).

5. **Conclusion**:
The minimum value of \( |z - 2.8| + |z - 1.42| \) is \( \boxed{1.38} \).