Convert in the form of (a + `i`b) :
3(1+i)-2(2+3i)

Explanation

To convert the expression \(3(1+i) - 2(2+3i)\) into the form \(a + ib\), we will follow these steps:

### Step 1: Distribute the constants
We start by distributing the constants in the expression:
\[ 3(1+i) - 2(2+3i) \]
This means we multiply \(3\) with both \(1\) and \(i\), and \(-2\) with both \(2\) and \(3i\).

### Step 2: Perform the multiplications
Calculating each part, we have:
\[ 3(1) + 3(i) - 2(2) - 2(3i) \]
This simplifies to:
\[ 3 + 3i - 4 - 6i \]

### Step 3: Combine like terms
Next, we combine the real parts and the imaginary parts:
- Real parts: \(3 - 4 = -1\)
- Imaginary parts: \(3i - 6i = -3i\)

So, we have:
\[ -1 - 3i \]

### Step 4: Write in the form \(a + ib\)
Now, we can express this in the form \(a + ib\):
\[ -1 - 3i = -1 + (-3)i \]
Here, \(a = -1\) and \(b = -3\).

### Final Answer
Thus, the expression \(3(1+i) - 2(2+3i)\) in the form \(a + ib\) is:
\[ -1 - 3i \]

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