Find the values of `x and y`: (i) `x+3i=6-9iy` (ii) `(x+iy)-(3-2i)=5+i` (iii) `i=x+2yi` (iv) `4x+i(x-y)=2-5i` (v) `(x+2iy)(2-i)^(2)=10(1-i)`

Explanation

Let's solve the equations step by step to find the values of \(x\) and \(y\).

### Part (i): \(x + 3i = 6 - 9iy\)

1. **Separate Real and Imaginary Parts**:
- Real part: \(x = 6\)
- Imaginary part: \(3 = -9y\)

2. **Solve for \(y\)**:
- From \(3 = -9y\), we get:
\[ y = -\frac{3}{9} = -\frac{1}{3} \]

**Values**: \(x = 6\), \(y = -\frac{1}{3}\)