Which of the following is the correct simplification of the expression `(2i -3) -(6+4i),` where `I = sqrt-1)` ?

Options

A. `-9-2i`
B. `-9+6i`
C. `-7-4i`
D. `3+ 6i`

Answer

To simplify the expression \( (2i - 3) - (6 + 4i) \), we can follow these steps:

### Step 1: Open the brackets
We start with the expression:
\[ (2i - 3) - (6 + 4i) \]
We can rewrite it by distributing the negative sign:
\[ 2i - 3 - 6 - 4i \]

### Step 2: Combine like terms
Now, we will combine the imaginary parts and the real parts separately. The imaginary parts are \( 2i \) and \( -4i \), and the real parts are \( -3 \) and \( -6 \).

- For the imaginary parts:
\[ 2i - 4i = -2i \]

- For the real parts:
\[ -3 - 6 = -9 \]

### Step 3: Write the final expression
Now, we can combine the results from the previous step:
\[ -9 - 2i \]

Thus, the correct simplification of the expression \( (2i - 3) - (6 + 4i) \) is:
\[ -9 - 2i \]