In the following, perform the indicated operations and write the result in the form x+iy:
(i) `(7-2i)-(3+2i)+(7+8i)`
(ii) `3-4i+2i-(8+7i)`
(iii) `(7-2i)-(4+i)+(-3+5i)`

Answer

Let's solve the given problems step by step.

### (i) \((7-2i)-(3+2i)+(7+8i)\)

**Step 1:** Distribute the negative sign in the first operation.
\[ (7 - 2i) - (3 + 2i) + (7 + 8i) = 7 - 2i - 3 - 2i + 7 + 8i \]

**Step 2:** Combine the real parts and the imaginary parts separately.
- Real parts: \(7 - 3 + 7 = 11\)
- Imaginary parts: \(-2i - 2i + 8i = 4i\)

**Step 3:** Write the final result in the form \(x + iy\).
\[ 11 + 4i \]

### (ii) \(3 - 4i + 2i - (8 + 7i)\)

**Step 1:** Distribute the negative sign.
\[ 3 - 4i + 2i - (8 + 7i) = 3 - 4i + 2i - 8 - 7i \]

**Step 2:** Combine the real parts and the imaginary parts separately.
- Real parts: \(3 - 8 = -5\)
- Imaginary parts: \(-4i + 2i - 7i = -9i\)

**Step 3:** Write the final result in the form \(x + iy\).
\[ -5 - 9i \]

### (iii) \((7-2i)-(4+i)+(-3+5i)\)

**Step 1:** Distribute the negative signs.
\[ (7 - 2i) - (4 + i) + (-3 + 5i) = 7 - 2i - 4 - i - 3 + 5i \]

**Step 2:** Combine the real parts and the imaginary parts separately.
- Real parts: \(7 - 4 - 3 = 0\)
- Imaginary parts: \(-2i - i + 5i = 2i\)

**Step 3:** Write the final result in the form \(x + iy\).
\[ 0 + 2i \]

### Summary of Results:
1. \(11 + 4i\)
2. \(-5 - 9i\)
3. \(0 + 2i\)