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Let's go through the problems step by step.

---

**16. Problem:**

\[
\text{Find the values of } x \text{ and } y \text{ such that } (2x + 2i) + (3y + 4x \cdot i) = 4 + 2i.
\]

We have to find \(x\) and \(y\) that satisfy this complex equation. Equating real and imaginary parts separately:

- **Real part:** \(2x + 3y = 4\)
- **Imaginary part:** \(2 + 4x = 2\)

From the imaginary part, we solve for \(x\):
\[
4x = 0 \quad \Rightarrow \quad x = 0.
\]

Substitute \(x = 0\) in the real part:
\[
2(0) + 3y = 4 \quad \Rightarrow \quad 3y = 4 \quad \Rightarrow \quad y = \frac{4}{3}.
\]

This doesn't match any of the given options, so there seems to be a different approach or misinterpretation of the question.

---

**17. Problem:**

\[
z_1 = x + yi, \quad z_2 = 6 + 8i, \quad \text{find } |z_1 + z_2|.
\]

The modulus \( |z_1 + z_2| \) is the magnitude of the complex number \(z_1 + z_2\). First, calculate the sum of \(z_1\) and \(z_2\):
\[
z_1 + z_2 = (x + 6) + (y + 8)i.
\]

Now, the modulus \( |z_1 + z_2| \) is:
\[
|z_1 + z_2| = \sqrt{(x + 6)^2 + (y + 8)^2}.
\]

Since we are not provided the values of \(x\) and \(y\), the answer depends on the specific values given. None of the exact values is clear, so we'd need further clarification.

---

**18. Problem:**

\[
\text{Multiply two complex numbers } (6 + 2i) \text{ and } (3 + 4i).
\]

Use the distributive property (FOIL method):
\[
(6 + 2i)(3 + 4i) = 6 \cdot 3 + 6 \cdot 4i + 2i \cdot 3 + 2i \cdot 4i
\]
\[
= 18 + 24i + 6i + 8i^2
\]
Since \(i^2 = -1\), the expression becomes:
\[
18 + 30i + 8(-1) = 18 + 30i - 8 = 10 + 30i.
\]

Thus, the result is \(10 + 30i\), but this isn't listed as an option. Perhaps there's a mistake in the options or formatting.

---

**19. Problem:**

\[
\frac{8 - 6i}{2}.
\]

Divide each part of the complex number by 2:
\[
\frac{8 - 6i}{2} = 4 - 3i.
\]

Thus, the answer is \(4 - 3i\).

---

Would you like more details on any of these problems or have any questions? Here are five follow-up questions based on this information:

1. Can you explain how to separate real and imaginary parts in complex equations?
2. How is the modulus of a complex number calculated?
3. What is the FOIL method for multiplying complex numbers?
4. How do you simplify expressions with \(i^2\)?
5. Can you explain division of a complex number by a real number?

**Tip:** When multiplying complex numbers, always remember that \(i^2 = -1\) to simplify correctly!

16. Nilai x dan y berturut-turut yang memberikan kesamaan (2x + 2i) + (3y + 4x i) = 4 + 2i adalah ... 17. Diketahui z1 = x + yi, 6 + 8i, dan z1 = z2, Nilai |z| adalah ... 18. Dua bilangan kompleks 6 + 2i, 3 + 4i bila dikalikan hasilnya adalah ... 19. √8 - 6i adalah ...

Explore solving complex number problems, including modulus, multiplication, and division of complex numbers, with step-by-step solutions for algebra students. These problems involve equating real and imaginary parts, using the modulus formula, and multiplying complex numbers.

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