https://r2.erweima.ai/mathbot/image/17265942337505tj1r54f.jpg

The question in the image asks for the modulus of the complex number \(5 + 12i\).

To calculate the modulus of a complex number \( z = a + bi \), the formula is:
\[
|z| = \sqrt{a^2 + b^2}
\]
where \(a\) is the real part and \(b\) is the imaginary part.

In this case:
- \(a = 5\)
- \(b = 12\)

Thus, the modulus is:
\[
|5 + 12i| = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13
\]

So, the modulus of the complex number \(5 + 12i\) is **13**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you calculate the modulus of a complex number in general?
2. What is the geometric interpretation of the modulus of a complex number?
3. How can we represent the complex number \(5 + 12i\) in polar form?
4. What is the argument (angle) of the complex number \(5 + 12i\)?
5. How do complex conjugates affect the modulus?

**Tip:** The modulus of a complex number is always non-negative and represents its distance from the origin in the complex plane.

O módulo do número complexo 5 + 12i é:

Learn how to calculate the modulus of the complex number 5 + 12i using the formula |z| = sqrt(a^2 + b^2). This detailed solution breaks down the steps and explains the concepts behind the calculation. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation