Here are the solutions to each of the questions:

1. Modulus of $-2 + 2i$:

   • Formula: $\text{Modulus} = \sqrt{(-2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$
   • Answer: b. 4

2. Calculation of $(4 + 2i) \times (-1 + 3i)$:

   • Formula: $(4 \times -1) + (4 \times 3i) + (2i \times -1) + (2i \times 3i)$
   • Calculation: $-4 + 12i - 2i + 6(-1)$
   • Final Result: $-4 - 6 + 10i = -10 + 10i$
   • Answer: b. -10 + 10i

3. Modulus of $7i$:

   • Formula: $\text{Modulus} = \sqrt{0^2 + 7^2} = \sqrt{49} = 7$
   • Answer: b. 7

4. Multiplication of $(-2 + 5i)$ with $(3 - 2i)$:

   • Formula: $(-2 \times 3) + (-2 \times -2i) + (5i \times 3) + (5i \times -2i)$
   • Calculation: $-6 + 4i + 15i + 10$
   • Final Result: $10 + 19i$
   • Answer: a. 4 + 19i

5. Multiplication of $5i$ with $2i$:

   • Formula: $5i \times 2i = 10i^2$
   • Calculation: $10(-1) = -10$
   • Answer: c. -10

6. Modulus of $(3 + 4i)$ multiplied by the modulus of $(4 - 3i)$:

   • Calculation: $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$
   • $\sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$
   • $\text{Product of Moduli} = 5 \times 5 = 25$
   • Answer: b. 25

7. Product of $(1 + 2i)$ and $(2 + 1i)$:

   • Formula: $(1 \times 2) + (1 \times i) + (2i \times 2) + (2i \times i)$
   • Calculation: $2 + 1i + 4i - 2 = 5i$
   • Answer: b. 0 + 5i

8. Modulus of $-1 - 1i$:

   • Formula: $\text{Modulus} = \sqrt{(-1)^2 + (-1i)^2} = \sqrt{1 + 1} = \sqrt{2}$
   • Answer: a. 2

9. Modulus of $-7 + 24i$:

   • Formula: $\text{Modulus} = \sqrt{(-7)^2 + (24i)^2} = \sqrt{49 + 576} = \sqrt{625} = 25$
   • Answer: a. 25

10. Modulus of $0 + 10i$:

    • Formula: $\text{Modulus} = \sqrt{0^2 + (10)^2} = \sqrt{100} = 10$
    • Answer: a. 10

Would you like more details on any of these questions?

Relative Questions:

1. How does the modulus of a complex number relate to its position on the complex plane?
2. What is the geometric interpretation of multiplying two complex numbers?
3. How does the modulus help in determining the magnitude of a vector represented by a complex number?
4. What is the significance of the imaginary unit $i^2 = -1$ when multiplying complex numbers?
5. How can you calculate the modulus of a complex number given in polar form?

Tip: The modulus of a complex number represents its distance from the origin on the complex plane, which is always a non-negative real number.