Complex conjugates are useful tools in math, especially when we work with complex numbers. Let’s break down how to use them in a simple way:

1. Simplifying Fractions: If you see a complex number in the bottom part of a fraction, you can make it easier to work with by multiplying both the top and the bottom by the complex conjugate.

   For example, to simplify the fraction (\frac{2 + 3i}{1 - i}), you can multiply by the conjugate (1 + i):

   $$\frac{(2 + 3i)(1 + i)}{(1 - i)(1 + i)} = \frac{(2 + 2i + 3i - 3)}{1 + 1} = \frac{-1 + 5i}{2} = -\frac{1}{2} + \frac{5}{2}i$$

   This makes it easier to see the answer.

2. Calculating Modulus: The modulus of a complex number, which looks like (z = a + bi), is found with (\sqrt{z \overline{z}}). Here, (\overline{z}) is the conjugate. This helps us understand how complex numbers relate to shapes in the complex plane.

3. Solving Equations: When solving equations that involve complex roots, it’s good to remember that these roots always come in pairs of conjugates. This can help you turn the problem into one with only real numbers.

Using these methods not only makes equations easier to solve but also helps you understand complex numbers better in math!