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### Problem 5: 
We are given three complex numbers:
- \( z_1 = 2 - i \)
- \( z_2 = 2i \)
- \( z_3 = 1 - i \)

We need to identify which operations among the options are correct:

- **Option A:** \( z_1 + z_2 = 2 - i + 2i = 2 + i \). This is **true**.
- **Option B:** \( z_1 - z_3 = (2 - i) - (1 - i) = 2 - i - 1 + i = 1 \). This simplifies to just 1, so **false**.
- **Option C:** \( z_1 \times z_2 = (2 - i) \times 2i = 2 \times 2i - i \times 2i = 4i - 2i^2 = 4i + 2 = 2 + 4i \). This is **false**.
- **Option D:** \( z_2 + z_3 = 2i + (1 - i) = 1 + i \). This is **true**.
- **Option E:** \( z_3 \times z_1 = (1 - i)(2 - i) = 2 - i - 2i + i^2 = 2 - 3i - 1 = 1 - 3i \). This is **true**.

So, the correct options are **A, D, and E**.

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### Problem 6:
We are given the complex number \( z = -3 - 3i \), and we need to determine which statements are correct:

- **Option A:** The polar form of \( z \). First, we find the modulus and argument:
  - \( |z| = \sqrt{(-3)^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \).
  - The argument \( \theta = \tan^{-1}\left(\frac{-3}{-3}\right) = \tan^{-1}(1) = 45^\circ \) (but it's in the third quadrant, so \( 180^\circ + 45^\circ = 225^\circ \)).
  Thus, the polar form is \( z = 3\sqrt{2}(\cos 225^\circ + i\sin 225^\circ) \), so **false** (the modulus in the statement is wrong).

- **Option B:** Exponential form \( z = 3\sqrt{2}e^{i225^\circ} \). This is **true**.

- **Option C:** The complex number as an ordered pair \( z = (-3, -3) \). This is **true**.

- **Option D:** The conjugate \( \bar{z} = -3 + 3i \). This is **true**.

- **Option E:** The principal argument \( \arg(z) = 135^\circ \). This is **false**; the correct argument is \( 225^\circ \).

So, the correct options are **B, C, and D**.

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Would you like more details or further explanation on any of these answers?

Here are 5 related questions to help expand your understanding:
1. How do you convert a complex number into polar form?
2. What is the general process to find the argument of a complex number?
3. How do you perform multiplication of two complex numbers?
4. Why is the conjugate of a complex number important in mathematics?
5. What are some applications of complex numbers in real-world problems?

**Tip:** Always remember to adjust the angle of a complex number based on its quadrant when finding the argument.

Diketahui z1 = 2 − i, z2 = 2i, dan z3 = 1 − i. Operasi bilangan kompleks berikut yang benar adalah...

Solve operations with complex numbers such as z1 = 2 − i, z2 = 2i, and z3 = 1 − i. This problem involves addition, subtraction, and multiplication of complex numbers, and covers key concepts such as polar and exponential forms. Suitable for students in Grades 11-12.

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