In the following, perform the indicated operations and write the result in the form x+iy:
`i^(3)+(6+3i)-(20+5i)+(14+3i)`.

Answer

To solve the expression \( i^3 + (6 + 3i) - (20 + 5i) + (14 + 3i) \) and write the result in the form \( x + iy \), we will follow these steps:

### Step 1: Simplify \( i^3 \)
We know that:
\[ i^2 = -1 \]
Thus,
\[ i^3 = i \cdot i^2 = i \cdot (-1) = -i \]

### Step 2: Substitute \( i^3 \) into the expression
Now substitute \( -i \) for \( i^3 \):
\[ -i + (6 + 3i) - (20 + 5i) + (14 + 3i) \]

### Step 3: Distribute the negative sign
Distributing the negative sign across the terms:
\[ -i + 6 + 3i - 20 - 5i + 14 + 3i \]

### Step 4: Combine like terms
Now, we will combine the real parts and the imaginary parts separately.

**Real parts:**
\[ 6 - 20 + 14 = 0 \]

**Imaginary parts:**
\[ -i + 3i - 5i + 3i = (-1 + 3 - 5 + 3)i = 0i \]

### Step 5: Write the final result
Combining the results from the real and imaginary parts, we have:
\[ 0 + 0i \]
Thus, the final result in the form \( x + iy \) is:
\[ 0 + 0i \]

### Summary
The result of the expression \( i^3 + (6 + 3i) - (20 + 5i) + (14 + 3i) \) is \( 0 + 0i \).

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