In the following, perform the indicated operations and write the result in the form x+iy:
`sqrt(3)+(sqrt(3)-2i)-(3-2i)`

Answer

To solve the expression \( \sqrt{3} + (\sqrt{3} - 2i) - (3 - 2i) \) and write the result in the form \( x + iy \), we will follow these steps:

### Step 1: Expand the expression
We start with the expression:
\[ \sqrt{3} + (\sqrt{3} - 2i) - (3 - 2i) \]

### Step 2: Distribute the terms
Distributing the negative sign across the last term:
\[ \sqrt{3} + \sqrt{3} - 2i - 3 + 2i \]

### Step 3: Combine like terms
Now we will combine the real parts and the imaginary parts separately:
- Real parts: \( \sqrt{3} + \sqrt{3} - 3 \)
- Imaginary parts: \( -2i + 2i \)

Calculating the real parts:
\[ \sqrt{3} + \sqrt{3} = 2\sqrt{3} \]
Thus,
\[ 2\sqrt{3} - 3 \]

Calculating the imaginary parts:
\[ -2i + 2i = 0i \]

### Step 4: Write the final result
Combining both parts, we have:
\[ (2\sqrt{3} - 3) + 0i \]
This can be expressed as:
\[ 2\sqrt{3} - 3 + 0i \]

### Final Answer
Thus, the result in the form \( x + iy \) is:
\[ 2\sqrt{3} - 3 + 0i \]

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