Let z

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.