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The problem asks to match complex numbers with their correct moduli.

### Formula for the modulus of a complex number:
For a complex number \( z = a + bi \), the modulus is:
\[
|z| = \sqrt{a^2 + b^2}
\]
Where \( a \) is the real part and \( b \) is the imaginary part.

### Now let's calculate the moduli for each complex number:

1. \( \sqrt{3} + 2i \)
   - Real part \( a = \sqrt{3} \), Imaginary part \( b = 2 \)
   - Modulus:
     \[
     |z| = \sqrt{(\sqrt{3})^2 + (2)^2} = \sqrt{3 + 4} = \sqrt{7}
     \]
   - Matches option 3 ( \( \sqrt{7} \) ).

2. \( 2 - \sqrt{5}i \)
   - Real part \( a = 2 \), Imaginary part \( b = -\sqrt{5} \)
   - Modulus:
     \[
     |z| = \sqrt{(2)^2 + (-\sqrt{5})^2} = \sqrt{4 + 5} = \sqrt{9} = 3
     \]
   - Matches option 2 ( \( 3 \) ).

3. \( -\sqrt{3} + \sqrt{2}i \)
   - Real part \( a = -\sqrt{3} \), Imaginary part \( b = \sqrt{2} \)
   - Modulus:
     \[
     |z| = \sqrt{(-\sqrt{3})^2 + (\sqrt{2})^2} = \sqrt{3 + 2} = \sqrt{5}
     \]
   - Matches option 1 ( \( \sqrt{5} \) ).

### Final Matches:
- A ( \( \sqrt{3} + 2i \) ) → 3 ( \( \sqrt{7} \) )
- B ( \( 2 - \sqrt{5}i \) ) → 2 ( \( 3 \) )
- C ( \( -\sqrt{3} + \sqrt{2}i \) ) → 1 ( \( \sqrt{5} \) )

Do you want more details or have any questions?

Here are 5 related questions for deeper understanding:
1. What is the geometric interpretation of the modulus of a complex number?
2. How can we calculate the argument (angle) of a complex number?
3. What is the difference between polar and rectangular form of a complex number?
4. How do the real and imaginary parts of a complex number affect its modulus?
5. Can a complex number with a negative imaginary part have a positive modulus?

**Tip:** Always square both the real and imaginary parts before summing them to compute the modulus of a complex number.

Tentukan modulus dari bilangan kompleks berikut: √3 + 2i, 2 - √5i, -√3 + √2i. Cocokkan dengan modulus yang sesuai dari pilihan: √5, 3, √7.

Learn how to calculate the modulus of the complex numbers √3 + 2i, 2 - √5i, and -√3 + √2i using the modulus formula. Step-by-step explanations provided for matching with the correct modulus choices: √5, 3, and √7.

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