`(3+4i)-(2+3i)`
Given that `I = sqrt-1,` what is the value of the expression above ?

Options

A. ` 1-i`
B. `1+i`
C. `1+7i`
D. `5 + 7i`

Answer

To solve the expression `(3 + 4i) - (2 + 3i)`, we will follow these steps:

### Step 1: Distribute the negative sign
We start with the expression:
\[ (3 + 4i) - (2 + 3i) \]
When we distribute the negative sign across the second set of parentheses, we get:
\[ 3 + 4i - 2 - 3i \]

### Step 2: Combine the real parts
Next, we combine the real parts of the expression:
\[ 3 - 2 = 1 \]

### Step 3: Combine the imaginary parts
Now, we combine the imaginary parts:
\[ 4i - 3i = 1i \quad (\text{or simply } i) \]

### Step 4: Write the final result
Putting it all together, we have:
\[ 1 + i \]

Thus, the value of the expression `(3 + 4i) - (2 + 3i)` is:
\[ \boxed{1 + i} \]

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