The given expression is \(\frac{1 - i}{2i}\), where \(i\) represents the imaginary unit. Let's simplify it step by step.

### Step 1: Multiply by the conjugate of the denominator
To eliminate the imaginary part in the denominator, multiply both the numerator and denominator by the conjugate of \(2i\), which is \(-2i\):

\[
\frac{1 - i}{2i} \times \frac{-i}{-i} = \frac{(1 - i)(-i)}{2i \cdot (-i)}
\]

### Step 2: Simplify the denominator
\[
2i \cdot (-i) = -2i^2 = -2(-1) = 2
\]

So the denominator becomes \(2\).

### Step 3: Simplify the numerator
Now, expand the numerator:

\[
(1 - i)(-i) = 1 \cdot (-i) - i \cdot (-i) = -i + i^2
\]

Since \(i^2 = -1\), the numerator simplifies to:

\[
-i - 1 = -(1 + i)
\]

### Step 4: Combine the results
Now, the expression is:

\[
\frac{-(1 + i)}{2} = \frac{-1 - i}{2}
\]

Thus, the simplified form of \(\frac{1 - i}{2i}\) is:

\[
\boxed{\frac{-1 - i}{2}}
\]

Would you like a more detailed explanation or have any questions?

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Here are 5 related questions to explore further:

1. How do you multiply complex numbers?
2. What is the geometric interpretation of multiplying by \(i\)?
3. How do you find the conjugate of a complex number?
4. How do you divide complex numbers in polar form?
5. Can you explain the properties of imaginary numbers?

**Tip:** When dividing complex numbers, always multiply by the conjugate to simplify the expression.

Learn how to simplify the complex expression (1 - i) / 2i step by step. This problem involves multiplying by the conjugate, applying properties of the imaginary unit, and simplifying complex numbers. Suitable for students in Grades 10-12.

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