Let m = Slope of the line `|z + 3|^(2) - |z-3i|^(2) = 24`, then m + 1.73 is equal to

Answer

To solve the problem, we need to find the slope \( m \) of the line defined by the equation \( |z + 3|^2 - |z - 3i|^2 = 24 \), where \( z = x + iy \).

### Step-by-Step Solution:

1. **Substitute \( z \)**:
Let \( z = x + iy \). Then we can express the moduli:
\[ |z + 3|^2 = |(x + 3) + iy|^2 = (x + 3)^2 + y^2 \]
\[ |z - 3i|^2 = |x + i(y - 3)|^2 = x^2 + (y - 3)^2 \]

2. **Set up the equation**:
Substitute these expressions into the given equation:
\[ (x + 3)^2 + y^2 - (x^2 + (y - 3)^2) = 24 \]

3. **Expand the squares**:
Expanding both sides:
\[ (x^2 + 6x + 9 + y^2) - (x^2 + (y^2 - 6y + 9)) = 24 \]

4. **Simplify the equation**:
Simplifying the left side:
\[ x^2 + 6x + 9 + y^2 - x^2 - y^2 + 6y - 9 = 24 \]
This reduces to:
\[ 6x + 6y = 24 \]

5. **Divide by 6**:
Dividing the entire equation by 6 gives:
\[ x + y = 4 \]

6. **Rearranging the equation**:
Rearranging gives:
\[ y = -x + 4 \]

7. **Identify the slope**:
The equation \( y = -x + 4 \) is in the slope-intercept form \( y = mx + c \), where the slope \( m = -1 \).

8. **Calculate \( m + 1.73 \)**:
Now, we need to find \( m + 1.73 \):
\[ m + 1.73 = -1 + 1.73 = 0.73 \]

### Final Answer:
Thus, the value of \( m + 1.73 \) is \( \boxed{0.73} \).