The variables 'real1', 'imag1', 'real2', 'imag2' have been initialized.

real1 is the real part of the first imaginary number (3 in the example above)

imag1 is the imaginary part of the first imaginary number (-7 in the example above)

real2 is the real part of the second imaginary number (1 in the example above)

imag2 is the imaginary part of the second imaginary number (-2 in the example above)

Task:  Appropriately initialize the variables (sumReal, sumImag, difReal, difImag, quoReal, quoImag) that correspond to the real and imaginary parts for the sum, difference, and quotient for the complex numbers given.

To initialize the variables `sumReal`, `sumImag`, `difReal`, `difImag`, `quoReal`, and `quoImag`, we'll perform the following operations on the two complex numbers represented by `(real1 + imag1*i)` and `(real2 + imag2*i)`:

### 1. **Sum of the Complex Numbers**
   - Real part: `sumReal = real1 + real2`
   - Imaginary part: `sumImag = imag1 + imag2`

### 2. **Difference of the Complex Numbers**
   - Real part: `difReal = real1 - real2`
   - Imaginary part: `difImag = imag1 - imag2`

### 3. **Quotient of the Complex Numbers**
   - First, calculate the denominator as the square of the modulus of the second complex number:
     \[
     \text{denominator} = \text{real2}^2 + \text{imag2}^2
     \]
   - Real part of the quotient:
     \[
     \text{quoReal} = \frac{\text{real1} \times \text{real2} + \text{imag1} \times \text{imag2}}{\text{denominator}}
     \]
   - Imaginary part of the quotient:
     \[
     \text{quoImag} = \frac{\text{imag1} \times \text{real2} - \text{real1} \times \text{imag2}}{\text{denominator}}
     \]

### Example Initialization:

Given the example values:
- `real1 = 3`, `imag1 = -7`
- `real2 = 1`, `imag2 = -2`

The initialization would be:
```python
sumReal = 3 + 1            # sumReal = 4
sumImag = -7 + (-2)        # sumImag = -9

difReal = 3 - 1            # difReal = 2
difImag = -7 - (-2)        # difImag = -5

denominator = 1**2 + (-2)**2  # denominator = 1 + 4 = 5
quoReal = (3*1 + (-7)*(-2)) / 5  # quoReal = (3 + 14) / 5 = 17 / 5 = 3.4
quoImag = ((-7)*1 - 3*(-2)) / 5  # quoImag = (-7 + 6) / 5 = -1 / 5 = -0.2
```

So the initialized variables would be:
```python
sumReal = 4
sumImag = -9
difReal = 2
difImag = -5
quoReal = 3.4
quoImag = -0.2
```

Would you like more details or have any questions about these calculations? Here are some related questions:

1. How do you multiply two complex numbers?
2. How do you find the modulus of a complex number?
3. What is the significance of the denominator in the quotient of two complex numbers?
4. How do you convert a complex number from rectangular to polar form?
5. How can complex numbers be used in electrical engineering?

**Tip:** When dividing complex numbers, it’s often easier to multiply by the conjugate of the denominator to avoid imaginary units in the denominator.

Learn how to initialize variables for operations on complex numbers including sum, difference, and quotient. This example covers the mathematical formulas for sum, difference, and quotient of complex numbers with given real and imaginary parts.

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