It seems like you're asking about complex numbers. Let's explore complex numbers in the context of the provided expressions, although the original expressions don't directly involve complex numbers. I can help explain complex numbers or solve problems that do involve them.

### What is a Complex Number?

A complex number is a number that has both a real part and an imaginary part. It is usually written in the form:

\[
z = a + bi
\]

Where:
- \(a\) is the real part.
- \(b\) is the imaginary part.
- \(i\) is the imaginary unit, defined as \(i^2 = -1\).

### Example of a Complex Number:

If you have \(z = 3 + 4i\), this means:
- The real part \(a\) is 3.
- The imaginary part \(b\) is 4.

### Operations with Complex Numbers:

1. **Addition/Subtraction:**
   \[
   (a + bi) + (c + di) = (a + c) + (b + d)i
   \]
   \[
   (a + bi) - (c + di) = (a - c) + (b - d)i
   \]

2. **Multiplication:**
   \[
   (a + bi)(c + di) = ac + adi + bci + bdi^2
   \]
   Since \(i^2 = -1\), the expression simplifies to:
   \[
   ac - bd + (ad + bc)i
   \]

3. **Division:**
   \[
   \frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{ac + bd}{c^2 + d^2} + \frac{bc - ad}{c^2 + d^2}i
   \]

### Imaginary Components in Your Equations:

While the original expressions provided in the problem don't include complex numbers, if you wanted to introduce complex numbers, you might encounter situations where the square root of a negative number

Explore the concept of complex numbers, their structure, operations (addition, subtraction, multiplication, division), and examples. Learn how to apply complex numbers in mathematical expressions and problem-solving. Suitable for advanced high school students and beyond.

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