Fir `i=sqrt(-1)`, what is the sum `(7+3i)+(-8+9i)`?

Options

A. `-1+12i`
B. `-1-6i`
C. `15+12i`
D. `15-6i`

Answer

To solve the problem `(7 + 3i) + (-8 + 9i)`, we will follow these steps:

### Step 1: Identify the real and imaginary parts
We can separate the real and imaginary components of the complex numbers:
- The first complex number is `7 + 3i`, where `7` is the real part and `3i` is the imaginary part.
- The second complex number is `-8 + 9i`, where `-8` is the real part and `9i` is the imaginary part.

### Step 2: Add the real parts together
Now, we will add the real parts:
- Real part: `7 + (-8) = 7 - 8 = -1`

### Step 3: Add the imaginary parts together
Next, we will add the imaginary parts:
- Imaginary part: `3i + 9i = (3 + 9)i = 12i`

### Step 4: Combine the results
Now we combine the results from the real and imaginary parts:
- The result is `-1 + 12i`.

### Conclusion
Thus, the sum of `(7 + 3i) + (-8 + 9i)` is `-1 + 12i`.

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