Question 1209625
Here's how to simplify the complex fraction:

1. **Simplify the innermost fraction:**

   1/i = (1/i) * (i/i) = i/i² = i/(-1) = -i

2. **Substitute back:**

   The expression becomes:

   1 / (1 - 1 / (2 - i))

3. **Simplify the fraction in the denominator:**

   1 / (2 - i) = (1 / (2 - i)) * ((2 + i) / (2 + i)) = (2 + i) / (4 - i²) = (2 + i) / (4 + 1) = (2 + i) / 5 = 2/5 + (1/5)i

4. **Substitute back again:**

   1 / (1 - (2/5 + (1/5)i))

5. **Simplify the denominator:**

   1 - (2/5 + (1/5)i) = 1 - 2/5 - (1/5)i = 3/5 - (1/5)i

6. **Rewrite the expression:**

   1 / (3/5 - (1/5)i)

7. **Multiply by the conjugate of the denominator:**

   (1 / (3/5 - (1/5)i)) * ((3/5 + (1/5)i) / (3/5 + (1/5)i)) = (3/5 + (1/5)i) / ((3/5)² - (1/5)²i²) = (3/5 + (1/5)i) / (9/25 + 1/25) = (3/5 + (1/5)i) / (10/25) = (3/5 + (1/5)i) / (2/5)

8. **Simplify:**

   (3/5 + (1/5)i) * (5/2) = 3/2 + (1/2)i

Therefore, the expression in the form a + bi is 3/2 + (1/2)i.