Determine the parameter K so that it is a real number and the following equation is maintained: Z= (1-2Ki)/(Ki). And the value of K so that it is a pure imaginary number.

1. Simplify the equation:
Z = \frac{1 - 2Ki}{Ki}
Z = \frac{1}{Ki} - \frac{2Ki}{Ki}
Z = \frac{1}{Ki} - 2
\frac{1}{Ki}=\frac{-i}{K}
Z=\frac{-i}{K}-2

2. For \(Z\) to be real:
The imaginary part must be zero:
\frac{-i}{K} = 0
Which happens when:
K \to \infty
Therefore, \(Z\) becomes:
Z = -2
Answer:

\boxed{K \to \infty}

3. For \(Z\) to be purely imaginary:
The real part must be zero:
-2 = 0
This is impossible.

Answer:

\boxed{\text{no finite } K}