To calculate the modulus (absolute value) of a complex number \( z = a + bi \), we use the formula:

\[
|z| = \sqrt{a^2 + b^2}
\]

Given \( z = 9 + 2i \), we have:

- \( a = 9 \)
- \( b = 2 \)

Now apply the formula:

\[
|z| = \sqrt{9^2 + 2^2} = \sqrt{81 + 4} = \sqrt{85}
\]

So,

\[
|z| = \sqrt{85} \approx 9.22
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the geometric interpretation of the modulus of a complex number?
2. How do you represent a complex number in polar form?
3. How do you add and subtract complex numbers?
4. What is the argument (angle) of \( z = 9 + 2i \)?
5. How do you multiply two complex numbers?

### Tip:
When calculating the modulus of a complex number, remember that the result represents the distance from the origin to the point in the complex plane.

Learn how to calculate the modulus of the complex number z = 9 + 2i using the formula |z| = sqrt(a^2 + b^2). This step-by-step solution involves basic complex number operations and the application of the Pythagorean theorem. Suitable for students in Grades 10-12.

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