Convert each of the following in the form of (a + `i`b) :
(i) `3(1+i)-2(2+3i)`
(ii) ` (1)/(4-5i)`
(iii) `(1-2i)^(-2)`
(iv) `(2-3i)/(3+5i)`
(v) `[(1)/(1-2i)+(3)/(1+i)][(3+4i)/(2-4i)]`

Explanation

Let's solve each part of the question step by step.

### (i) Convert `3(1+i)-2(2+3i)` to the form of (a + ib)

1. **Distribute the constants:**
\[ 3(1+i) = 3 + 3i \]
\[ -2(2+3i) = -4 - 6i \]

2. **Combine the results:**
\[ 3 + 3i - 4 - 6i = (3 - 4) + (3i - 6i) = -1 - 3i \]

3. **Final result in the form (a + ib):**
\[ -1 - 3i \]