To find the modulus (or absolute value) of a complex number, follow these steps:

### Steps to Find the Modulus of a Complex Number

1. **Write the Complex Number**:
   - A complex number is usually written in the form \( z = a + bi \), where \( a \) is the real part and \( b \) is the imaginary part.

2. **Apply the Modulus Formula**:
   - The modulus of the complex number \( z = a + bi \) is given by:
     \[
     |z| = \sqrt{a^2 + b^2}
     \]
   - This formula is derived from the distance formula in the complex plane, where the modulus represents the distance from the origin (0, 0) to the point \( (a, b) \) in the plane.

3. **Calculate the Modulus**:
   - Square the real part \( a \) and the imaginary part \( b \).
   - Add the squares.
   - Take the square root of the sum.

### Example

Let's find the modulus of the complex number \( z = 3 + 4i \).

1. **Identify \( a \) and \( b \)**:
   - Here, \( a = 3 \) and \( b = 4 \).

2. **Apply the Modulus Formula**:
   \[
   |z| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
   \]

So, the modulus of \( z = 3 + 4i \) is **5**.

Would you like more details or have any questions? Here are five related questions:

1. How does the modulus of a complex number relate to its graphical representation?
2. What is the modulus of a purely imaginary number, like \( 0 + bi \)?
3. How would you find the modulus of a complex number given in polar form?
4. What is the effect of conjugating a complex number on its modulus?
5. How does the modulus help in dividing complex numbers?

**Tip:** The modulus is always a non-negative real number and represents the distance from the origin to the point representing the complex number in the complex plane.

Learn how to find the modulus of a complex number with a detailed step-by-step guide. Understand the formula |z| = sqrt(a^2 + b^2) and its application. Suitable for advanced high school students and anyone interested in complex numbers.

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